Would versus Will

I'm afraid that you are both a bit off the mark.

We will extend all support required-- a simple statement of intention.  Since the email is not a contract, there is no fear of contradiction if it happens that some query cannot be addressed.  Will here is a positive statement of intended helpfulness.

We would extend all support required [if such is requested of us].  This is the full form of the sentence, and it is a conditional statement-- conditional on the reader's submission of a query, not the ability of the writer to address said query.  Would here is slightly more polite (as it suggests that queries are not required, but are at the pleasure of the reader), but I think that in this situation, the more upbeat will is more appropriate.

The similarity is that these are all modal verbs.  Each gives a slightly different shade of meaning, or even multiple meanings to the surrounding thought.

Why should I ...  asks why I am obligated to do something, or why it is expected of me to do it (possibly even with the flavor that I think it is unjust to have to do it -- if said in a whining tone!).

Why would I ... asks in which possible world or under what conditions there is a reason to do something (possibly with the suggestion that there is no such set of circumstances I can think of).

What should be ... asks which answer is expected or fitting in the given situation.

What would be ... asks for the answer under some implied circumstances, unstated, resulting in a more remote (and therefore more polite, perhaps) way of asking "What is the answer?"

CJ

Yes.  I agree that that's a good addition.