Shall/will and should/would [LONG AND SOO BORING]

Among my reference books of English is "A Practical English Grammar" by Thomson and Martinet, a must-have for teachers. 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, rather conservative sometimes.
I've already asked this group for advice as to the question "shall/will; should/would"; still I would like to ask you again now that I've clarified things about it.
On "A Practical English Grammar" I learn this, more or less (I note that in this post I'll never mean "should" as the modal to express conditional duty):
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 equivalent to "shall", 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).
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, 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).
you shall
he shall
you shall
they shall
Used only in contracts to express duty.
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...

Moreover, "A Practical English Grammar" has an entry dealing with "I should/would think so". Since in that grammar book it reads "I should/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?
Should I say "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"?
Another question about shall/will and should/would: I've always used, up to 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.../I should like..." (together with "I will/would") and just avoiding both of them? Or is it possible to use "I shall/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 entirely, at least).

Thank you very much for standing such a complicated post!
Bye-bye, FB (corrections are always welcome. Punchs and kicks are not.)