They’d kill off the probiotic but not all of them so it’s better to eat your good yogurts still even when on an antibiotic. So said my gastroenterologist. Also it’ll help your gut flora bounce back quicker.

Antibiotics tend to kill more bacteria than just the bad ones you’re trying to kill, so yes. While taking antibiotics (and afterwards), you should take probiotics to replace good ones that are getting killed, and help out your digestive tract during the treatment. They won’t interfere with the antibiotic killing the bad bacteria that it’s targeting.

Yes

They either cancel each other out - or cancel you out

It would depend on the specific antibiotic and specific probiotic. Each antibiotic will kill a certain subtype of bacteria (ex. Those that have a certain type of shell). So it’s possible that they will go their separate ways, or you’ll waste both by reenacting osmosis jones.

Now this second part is something I’m not sure about. I used to think that it makes sense to have probiotics after an antibiotic treatment is complete, since you can repopulate your gut with healthy bacteria once the harmful bacteria has been eradicated. However apparently the science isn’t settled on that: https://www.bbc.com/future/article/20190124-is-it-worth-taking-probiotics-after-antibiotics

No Stupid Questions is over here