Two rain related issues

I have a 2001 V6 automatic with 158,000 miles.

When it is raining and I press the keyfob to unlock or lock the door, it doesn't make the beep sound. The doors still lock/unlock, but there is no sound. When the truck dries again the beep sound comes back. I've had that issue for a long time and I am not sure that is a big deal, since the beep is a little annoying, but I wonder if anyone has any idea why the beep sound goes away?

The last couple of times it has rained, however, I have been having another problem when I first start up the truck and put it in gear, the truck sputters. Now, when the truck warms up, the sputtering goes away. Presumably the problem is something related with the spark plug wires or injector coils. Any ideas how to check?

Thanks,
Steve