1. Modes of future reference
What would be the difference in the following?
a. Elmegyek a boltba
b. Fogok menni a boltba (and does reversing the fogok and menni convey any subtle difference in meaning?)
c. El fogok menni a boltba
I realise that in everyday speech one tends to use longer sentences and a lot is deduced by context as well.

a. Elmegyek a boltba. It means two things:

I have the intention to go to the shop right now (I’m going to the shop).

and

I promise I will go to the shop, but not right now (I’ll go to the shop).

b. Fogok menni a boltba. It sounds more like one action of a list.

Fogok tévézni, házit írni, aztán fogok menni a boltba…
I’ll watch tv, write my homework, then I’ll go to the shop…

If you ask ’Fogsz menni a boltba?’, it means that you’re wondering if the person you asked even has the intention to go or not. You don’t really care if he buys milk or not. The result is not important.

c. El fogok menni a boltba. This is a strong intention.

I’m (definitely) going to the shop. It is my firm will to do so.

If you ask ’El fogsz menni a boltba?’, it means that you want to know how it ends. You expect the person you asked to say yes because you’ve run out of milk and if he goes to the shop, he can buy milk, bring it home and you have it again. So you want that his going to the shop be accomplished. It is the result that counts.

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2. Does Hungarian have subtle ways of expressing future perfect, future perfect progressive, pluperfect, pluperfect progressive using coverbs, or is it more about knowing the entire sentence and deducing by context?

Coverbs are really not there to add shades to tenses. All day can do is indicating direction literally and figuratively and change the meaning of a verb in a subtle or radical way. However, there is absolutely no possibility for them to ”insert” subtle changes in how we perceive the way a tense expresses time.

FUTURE PERFECT SIMPLE

As a matter of fact, there are three tenses you can use in Hungarian for Future Perfect: present, past and future (periphrased with the auxiliary verb ’fog’).

Let our basic sentence be:

I will have extinguished the fire by the time the firemen arrive.

’I will have extinguished’ is Future Perfect. This English tense expresses the fact that someone will do something that is done/finished in the future by the time a certain event happens. So this is really an event in the past of th future. The action expressed with Future Perfect happens before the action introduced by the conjunction ’by the time’ in the subordinate clause.

Let’s see how you can translate it in Hungarian.

a.
Mire a tűzoltók megérkeznek, (addigra) már eloltom a tüzet.
b.
Mire a tűzoltók megérkeznek, (addigra) már eloltottam a tüzet.
c.
Mire a tűzoltók megérkeznek, (addigra) már el fogom oltani a tüzet.

The literal translation for the three sentences would be:

a.
By when the firemen arrive, (by that time) I already extinguish the fire.
b.
By when the firemen arrive, (by that time) I already extinguished the fire.
c.
By when the firemen arrive, (by that time) I will extinguish the fire.

What we realize instantly is that the sentence is reversed. Hungarian likes to say such sentences in this order for some reason. It just sounds better. Although I don’t know any rules that forbid English to do the same.

By the time the firemen arrive, I will have extinguished the fire.

It doesn’t sound that bad at all. 

So you have three tenses to work with when it comes to translate Future Perfect.

I have to admit, though, that the past tense sounds better and more powerful. Because it expresses a finished action in the past, it is more suitable to express the same concept regarding the future. Despite that, I recommend you use present and past tense alternately.

You can emphasize the action expressed with the past tense by using már (already), rég (long ago).

The main clause can be expressed by the present and past tense. True enough the present tense is much more in use.

I’ll have repaired the roof by the time the rain comes down.
Mire leesik az eső, befoltozom a tetőt.
Mire leesik az eső, márbefoltoztam a tetőt.

The children will have arrived by the time the lunch is done.
Mire megfő az ebéd, a gyerekek is megérkeznek.
Mire megfő az ebéd, már a gyerekek is megérkeztek.

Winter will have arrived by the time you finish digging up the garden.
Mire elkészültök a kert felásásával,beköszönt a tél.
Mire elkészültök a kert felásásával, már régbeköszöntött a tél.

You can use the antecedent addigra (by that time) if you feel like so. It is not necessary.

Mire leesik az eső, addigra már befoltoztam a tetőt…and so on.

Mire is a synonym for amikorra which literally means by when.

FUTURE PERFECT PROGESSIVE/CONTINUOUS

This tense expresses the same thing as Future Perfect, except it refers to actions in progress. An action that was/will be started in the future and is still continued.

Tomorrow I’ll have been working in the office for two years now.

Such sentences can be translated in Hungarian in two ways:

First Solution:

Adverb of Time + lesz + TIME EXPRESSION + hogy + Present Tense

HolnapleszKÉT ÉVE, hogy a hivatalban dolgozom.
TomorrowI’ll have been working in the office FOR TWO YEARS NOW.

The literal translation is:

Tomorrowit will be TWO YEARS that I work in the office.

The time expression has the possessive suffix –(j)e, -(j)a and here’s why. This is the absolute literal translation of such Hungarian sentences:

Tomorrowit will be TWO YEARS of the fact that I work in the office.

You see ’of the fact that’, which refers to a certain relationship (possession) between the two years and my working in the office.

So far so good. But what if there are more time expressions?

Tomorrow next weekI’ll have been working in the office FOR TWO YEARS NOW.

You see ’tomorrow next week’ forms a unit and then we have ’for two years now’ at the end of the sentence. The translations can be:

Holnaphoz egy hétre már KÉT ÉVEdolgozom a hivatalban.
Holnaphoz egy hétreleszKÉT ÉVE, hogy a hivatalban dolgozom.

More examples:

This time next year I’ll have been learning Spanish for three years.
Mához egy évre már három éve tanulok spanyolul.

Két nap múlva lesz hat hónapja, hogy leveleket írok neked.
In two days I’ll have been writing you letters for six month now.

PAST PERFECT AND PAST PERFECT PROGRESSIVE

When there are two actions in the past, this tense and its continuous/progressive brother express the action that happened before the other action. The conjunction is usually: after (miután), before (mielőtt).

Afterthe boy had crossed the road, the girl ran after him.
Miután a fiú átment az úton, a lány utána futott.

Before the girl ran after the boy, hehad crossed the road.
Mielőtt lány utána futott, a fiú már átment az úton.

You see that Hungarian uses its one and only PAST TENSE to express both Past Simple and Past Perfect.

For a Hungarian, it is obvious that the boy did his action before the girl did hers. IT IS ALL IN THE CONTEXT, logic and common sense. Plus the conjunction miután also helps us figure things out. That’s why Hungarian doesn’t need more past tenses.

As Past Perfect Progressive is no different, only that it refers to a continuous action, I’ll just give you some more examples for both.

My mom had been ironing my shirt when I stepped inside.
Anyukám már vasalta az ingemet, amikor beléptem.

The mechanic was asking for his money before I even asked if he had repaired the car.
Az autószerelő a pénzét kérte, mielőtt megkérdeztem, hogy megjavította-e az autót.

The postman was tryingto drop the letter in the mail-box after he had rung the bell.
A postás próbálta bedobni a levelet a postaládába, miután csengetett.

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3. My final question(s) is more to you personally about Hungarian teaching.

a. Although in strict grammatical terms Hungarian is described as having 2 tenses (past and non-past), do you think it is fairer to say hungarian actually has more, but a better way of expressing this would be 'tense equivalents'?

It is more correct to say that there is a past and present-future tense. Because our present tense can refer to future actions, just as well as to present actions.

b. If you agree with the above do you think Hungarian resources need to describe this better (like the way you do in this blog)? I ask this as coming from an English/Welsh speaking background, where both languages have a huge array of expressing tense/aspect it is quite a leap for a beginner in Hungarian to try to adapt to thinking in terms of these! (I guess this exemplifies the big difference in Indo-European linguistic psychology and Uralic/Ugric linguistic psychology!).

I agree that we should have better and much more in-depht explanations. Unfortunately, I haven’t seen much of that, not even from authors ’held in high esteem’.

c. Do you find that a lot of Hungarian language references seem to only briefly describe coverbs and their uses, yet given how crucial they are they should get a lot more chapters devoted to them?
Personally I don't think there is too much of a problem integrating coverbs with chapters on teaching past/non-past tenses as this would seem more logical for beginners grappling with tense/aspect who come from non-Uralic language backgrounds.

It is absolutely necessary to teach coverbs from the very beginning. Just as crucial as in English. After all it is not the same to say:

I’m getting on well with him OR I’m getting on with my life.

Again, not much material I’ve seen from professionals so far.

In my opinion, it is important to learn that meg-, el-… can express perfectivity, completeness. The rest is a memorizing process. Mainly learning the shades of meaning because coverbs don’t have an impact on the meaning of any tense. Coverbs define if the verb has a complete or a continuous aspect.

Kikészítem a ruhámat az ágyra. (I’ll put my clothes ready on the bed.)
Kikészítettem a ruhámat az ágyra. (I put my clothes ready on the bed.)

Ki-(out) indicates the direction. I had to take the clothes from the inside of the wardrobe so that I could put them out on the bed. And it also gives completeness to my action in the past tense.