The original questioner's assumption is correct: in normal conversation 'shall' is only used in First person singular and plural, mainly in offers and suggestions and their related question tags - 'I'll open a window, shall I?', 'Lets go out tonight, shall we?'

In British English, it is also used interchangeably with 'will' in First person singular and plural, with no change of meaning (although there used to be a distinction in the past). 'We will / shall just have to wait and see'. I do this, but this use of 'shall' is declining.

In legal English, however, 'shall' is also used in the Third person, to denote obligation (it seems shall is used for people, must for things) - 'The tenant shall keep the apartment in good order, and the rent must be paid by the allotted day each month', 'The parties to this contract shall abide by the conditions herein and all aforesaid conditions must be adhered to'.

In the example - 'Company A shall have contributed 50 million dollars to the joint venture.' the only way I can read this is as a Future perfect, with this element of obligation. But something is missing - the date by which this obligation must be fulfilled
- 'By the date set out in Clause 3 of said contract, Company A shall have contributed 50 million dollars to the joint venture.' In other words, Company A must contribute that sum before the date specified.

This is confirmed in a discussion document on legal English, where the writers quote an authority talking about "the use of the perfect infinitive after shall as denoting  ‘...events expected to be completed by a certain time in the future’ and give the example sentences: 

‘The Fund shall have performed all obligations required  to be performed by  it' 
'Buyer shall have received a certificate on behalf of the Fund to such effect.’ "

As to the old distinction, the two forms were apparently used in (S.E.) England in opposite ways, depending on the grammatical person:

First person - will = wishes, desires, shall = simple futurity
Second and Third persons - will = simple futurity, shall = obligation (hence the legal sense)

This explains this rather obscure linguistic joke: 'There was a non-English speaker of English (variously portrayed as French, Scottish, or Irish) who was drowning and cried out “I will drown; no one shall save me!”. The idea being that nobody would save him, because they thought he meant - 'I want to drown; no one should save me'.

What he should have said, of course, was 'I shall drown; nobody will save me', where both 'will' and 'shall' refer to simple futurity. Obvious, isn't it?

Fowler wrote quite a bit about this, but noted sadly 'It is unfortunate that the idiomatic use [of shall], while it comes by nature to southern Englishmen (who will find most of this section superfluous), is so complicated that those who are not to the manner born can hardly acquire it'. Nowadays, I doubt even a southern Englishman would make or even recognise the distinction.

I've written more about this here:

http://random-idea-english.blogspot.com/2010/12/do-you-think-people-will-still-say.html

I think we need auto-linking for https addresses!

At the British National Corpus:
enamoured of 50
enamoured with 10
enamoured by 4

http://www.natcorp.ox.ac.uk/

At Netspeak (web based - so international)
enamoured of 61%
enamoured with 22%
enamoured by 6%

enamored with 44%
enamored of 40%
enamored by 8%

http://www.netspeak.org/#query=enamoured+%253F

Which suggests that Brits favo(u)r 'of' while North Americans favo(u)r 'with' (in which case I'm a traitor, as I go for 'with' for people, and 'of' for things)

In books though, 'of' seems to win in both dialects:

https://books.google.com/ngrams/graph?content=enamored+of%3Aeng_us_2012%2Cenamored+with%3Aeng_us_2012%2Cenamoured+of%3Aeng_gb_2012%2Cenamoured+with%3Aeng_gb_2012&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cenamored%20of%3Aeng_us_2012%3B%2Cc0%3B.t1%3B%2Cenamored%20with%3Aeng_us_2012%3B%2Cc0%3B.t1%3B%2Cenamoured%20of%3Aeng_gb_2012%3B%2Cc0%3B.t1%3B%2Cenamoured%20with%3Aeng_gb_2012%3B%2Cc0

@Teacher Habib - In Third person singular, 'has' is used when the verb 'have' is the main verb - 'He has a large house', or is the auxiliary in Present perfect - 'He has already spoken to the boss' or Present perfect continuous - 'He has been cleaning the car.'

But in your example - 'He will have taken his food', we have Future perfect where 'have' is used together with the modal verb 'will', and modal verbs are always used with the base form of the verb, which is 'have' - 'He might have time later on', 'She could have been wrong', 'He must have forgotten to do it'.

The same thing happens in Future continuous, where we use the base form 'be', not 'is'- He will be having his lunch then, so better phone later'.

We can also have a Future perfect continuous (the most exotic tense), combining 'will', 'have' and 'be' - 'By the end of next month, he'll have been working here for ten years'.

By the way, your example isn't very natural in Standard English, although it almost works in Scottish English - 'You'll have had your tea.' (which really means 'I don't want to make you any tea'). Better might be something like 'He'll have finished eating by then'.

@jayles - re your third paragraph - absolutely. The first thing I found here was that it wasn't the long words (i..e Latinates) they found difficult, but the short ones, and especially phrasal verbs.

I'm not really au courant with modern education in Britain; it's just the impression I get from reading the papers.

I don't do any academic English teaching myself, although I have done a little IELTS, so I'm not really aware of these problems, but you might be interested in this little 'tool' I put together:

http://random-idea-english.blogspot.com/2013/04/finding-language-in-context-academic.html

@T_reason - if there was (were for subjunctive freaks) no such word as legos, this discussion wouldn't be taking place. The fact that a lot of people use it, including people like the LA Times and NPR, has, by definition, made it a word. How else would you describe it?

http://www.latimes.com/business/technology/la-fi-tn-one-mans-quest-to-prove-legos-can-be-used-to-make-art-20131014,0,5081534.st

http://www.npr.org/blogs/monkeysee/2013/06/28/196605763/girls-legos-are-a-hit-but-why-do-girls-need-special-legos

@jayles - I think you're making false comparisons. Obviously people who learn Latin and Greek aren't studying it as a means of social communication; they have other reasons for doing so. Nobody that I know of is suggesting that someone should learn Latin or Greek instead of Spanish or any other modern language. One does not rule out the other. In fact it might complement the other. It's quite possible my vague memories of Latin helped when it came to learning French and Spanish.

And although knowledge of Latin is of course not necessary for an understanding of English, it certainly makes it more interesting for me, as does a bit of French. But then, unlike you, I relish English's bastard roots.

What has stopped people learning modern languages in Britain has nothing to do with people learning Classics, but the removal or reduction of language teaching from the core curriculum and from university entrance requirements, and the general attitude to learning foreign languages in Britain. In Poland everybody learns a second language, and many of my students a third, and many universities demand a second language. This is quite standard in continental Europe, but I never hear any complaints that this policy might suffer from the teaching of Latin.

I really think you're complaining about a problem that doesn't exist. How many people are made to learn Latin at school nowadays, and of those, do we really know that it's at the expense of modern languages?

@jayles - for someone who thinks learning Latin and Greek is a waste of time, you seem to know an awful lot about them (and be rather interested in them). Are they, then, also a waste of your time?

@Aurie - And indeed the French were somewhat nonplussed at all the fuss over French Fries / Liberty Fries after their 2003 veto, as they also considered 'frites' to be a Belgian concoction. In the last couple of years here in Poland, Belgian 'frites' have become all the rage.

http://www.visitbelgium.com/?page=frites

@Brus - To be honest I'm not sure I'd even made the connection between opus and opera, or if I had, I'd forgotten about it. Thanks for that, and for the rest. And to add to the list, we have of course, corporal and corporeal.