Three questions about modal verbs

I have already posted this on alt.usage.english, but I didn't get any answer. I thought I would be better off asking here.
1) Among my reference books of English is "A Practical English Grammar" byThomson and Martinet, a must-have. I have found interesting the parts dealing with the conditional, which has often given me a hard time as I have always tried to comply with the British English standard, more demanding than the american.
On "A Practical English Grammar" (as well as "Practical English Usage" and other books) I've learnt this, more or less (I note that in this post I'll never mean "should" as the modal verb to express conditional duty but as the modal auxiliary verb as an alternative to "would" for first persons):

Future
I shall/will
you will
he will
we shall/will
you will
they will
where "I/we shall" carries a plain future meaning and "I/we will" expresses volition, it being understood that in current use "will" may be just equivalent
to "shall" (especially in American English, which doesn't use "shall" at all, if not for such set phrases as "Let's do it, shall we?"), the latter being used only in ambiguous cases.
Besides, "will" doesn't necessarily express a future action, but also a present strong will with all persons (not only I/we): "He won't tell you anything!".
Conditional
I should/would
you would
he would
we should/would
you would
they would
Here Thomson and Martinet, if I recall correctly, don't say that "I/we should" expresses a plain conditional meaning, whereas "I/we would" carries a conditional will (the same way as shall/will), but I assume the authors have let it be understood.
Even with the conditional, "would" may be used to express a conditional will (with all persons): "She wouldn't tell us nothing, unfortunately".
you shall
he shall
you shall
they shall
Used only in contracts to express duty. In the past it was used to make promises etc.
What's the matter? First of all I should (oops... I would) appreciate if you would tell me whether what I've just written is right, wrong, shameful...
2) Moreover, "A Practical English Grammar" has got an entry dealing with "Ishould/would think so". Since in that grammar book it reads

I should/would
you would
he would
we should/would
you would
they would
in all the chapters about the conditional, I assume that the "should" in "I should think so" is just an ordinary conditional, where one may use either "should" or "would" for the first persons (in British English). If so, considering that the conditional with should (for the first persons) is getting less and less common, why is "I should think so" that established whithin the English people (rather than "I would think so")? Should I say, as a non-native speaker, "I would think so" (which is quite right) just like I say "If I
were you, I would..." or "I would like...", or had I better handle "I should* think so" as a set phrase? I'd say the latter, still it sounds to me like a person pretending to be educated having the opposite effect. I mean, if I say "I would like" and "I would appreciate", where's the sense in "I *should think so"?
3) Another question about shall/will and should/would: I've always used, upto
now, either "shall" or "will" with the first persons, but now I'm beginning to suspect that this distinction is inconsistent, as I do not use, conversely, either "should" or "would" to form the conditional. Do you think I ought to choose between using either "I shall do that" or "I
should like" (together with "I will do that" and "I would...", with different shades of meaning) and just avoiding both of them? Or is it possible to use either "I shall" and "I will" and still to form the
conditional with "would" only without sounding awkward or uneducated? I make no secret that I might decide just to forget "shall" (and it might be best, in a future perspective), though this topic seems very interesting to me (am I sane? I should/would think not quite, at least), apart from the positive advantages.
Thank you very much for standing such a complicated post!
Bye-bye, FB (corrections are always welcome. Punchs and kicks are not.)