If Hitler keeps, at least temporarily, the Munich agreement, how does this affect British, French (and even American) rearmament. Britain and France accelerated their rearmament after Munich collapsed.
Correct, they made a effort to accelerate. However The Munich Crisis was a important wake up call it self & the subsequent agreement was not used as a excuse to stand down. Internally within Chamberlains cabinet the agreement that defused the crisis was seen as buying time for the already started rearmament program to produce results. As with the French cabinet Chamberlains government took seriously the pronouncements of their Marshals that their nations were near defenseless against the German military might of 1938. Rearmament programs had already been kicked off when the nazi government began building the Wehrmacht in 1934, those were added to after the Rhineland occupation in 1936, and the Austrian Anschluss of 1937. At the end of the 1920s the French made the decision to invest 7,000,000,000+ Francs in a defense system to counter a hypothetical German army of less than 500,000 light infantry. Even before the Munich Crisis France had laid out a rearmament program to prepare for total war against German NLT 1942.
Remember that the Spanish war & Japanese invasion of China were concurrent to all this. The French and British leaders had repeated emerging examples of just what modern warfare implied & what was really required for defense. While the electorate was increasingly terrified and demoralized by the threat the leaders took with increasing urgency the proposition that war would be underway in 2-3 years.
While the Battle of France was obviously not positively affected by any such acceleration what about the Battle of Britain? Would the air defenses of the UK been where they were OTL if Munich had not collapsed or would they have been just enough "delayed" so that the Luftwaffe does better?
Not really the funds, orders, and schedules were in place in the Autumn/Winter of 1938. It had been a nasty shock to the cabinet & Parliament when told the RAF could not defend London from air attack. The near panic among the leadership before the Munich meeting led to determination to restore military superiority if at all possible, and to the decision to buy time with Czech territory. This applied as much to the French government as the British.
... Suppose Hitler demands a change in the Polish corridor/Danzig but now he has "kept" his agreements??
One example hardly offsets all the other broken agreements. The abrogation of reparations payments, rearmament, reoccupation of the Rhineland, the Austrian annexation, abrogation of economic agreements like the Young Plan. The nazi government from the start was really good at reassuring their intent to honor treaties & agreements, then a few months, or even weeks later tossing another "scrap of paper" in the waste can. In the weeks leading up to 1 September 1939 there had been reassurances that renegotiation of the German/Polish issues was sought, nothing more. Then abruptly what could only be described as a war of destruction was launched.
As you know the German demands were far more than the Danzig corridor, that Polish government agreed to negotiate it all, and the Anglo French governments backed that willingness to negotiate. The Poles halted the mobilization of their armies reservists, & otherwise avoided some key actions that would have been seen as provocative. Simply that the German armies attacked at all was a shock to the Anglo/French governments, and about everyone else. That from day one the attack was not a limited one to gain some bargaining power was a further indicator to the Allies. Both Britain and France had enough intelligence on the Wehrmacht to understand forces sufficient to destroy Poland were attacking, not something limited to just defeating the Polish army and pushing it back a bit. If there were any residual doubts at the end of the first week the air attacks on Warsaw & other cities further dispersed the idea of a limited negotiating gambit.