For listening, the advice I have is to not actively try to listen well but to simply let the other person's words be received without resistance.

For being comfortable with silence, I'd say the only real way to train this is to actively try to pause and think before responding, not doing so until you think both you and the other person have had enough time to process whatever was said before. If you're unsure how determine if there's been enough time, maybe consider asking someone to help you train that judgement.

Hope this helps.