My $.02.
Sitch #1:
Whistles sound at the exact same time. I hate it when that happens.
If I were you I would have gone to partner and said we had a time out by coach A. If your partner insists on the 5 sec violation then go with it, but if your partner blew his whistle for the five second count after you recognized the coaches request (you recognized the coaches request before you blew your whistle) then I think you grant the T/O. The reason the coach requested the T/O was because he knew the count was at 4. That being said, the players should be coached to request timeout in that situation.
Sitch #2
I agree with Rut with regards to allowing for the game situation, (... be 100% sure it was first. You do not want to be wrong about that call.) In the origional post you said this foul occured at the end of the first quarter. If it is an obvious foul that occured before time expired, then report the foul. If it is a shooting foul or bonus situation then have the player shoot the throws with no time on the clock and the lane empty.