I have a very similar problem today; I thought I was doing the right
thing using the slow drip method to not have pipes freeze, but I now
have a leak from the end of the P trap. I'm wondering if I should try
to put hot water in the sink and if breaking up that ice will ease the
pressure on where the trap meets the next pipe.

Is it typical for water to stay standing in the P trap? I would guess
so, lots of rookie questions I have here.

Don't mean to hijack this thread, just joining in on the fun g.
jtr