First questions confused me. Are you asking if you can feel shit while doing anal? Most of the time you don't. Because of prep.
If you're asking if bottom feels like they are going to shit while getting dicked down... yes. Sometimes. Mostly to virgins who haven't had their cherry popped. But it's true that after training, that you can really feel it from anal & even cum.. and that weird feeling does go away after a few times.
For yer second question:
If you eat someone's ass, you might taste remnants. However if the person washes appropriately, typically you don't taste anything.

I hate to be that person who asks this but....does it feel like they're shitting up and down in their ass when getting the dihh? And do the top taste remnants of shit sometimes?