Can I take probiotics while taking Xifaxan in order to not have diarrhea or be susceptible to...

It is likely that if you take probiotics while on an antibiotic they will just be killed off by it right away. It’s possible that if you take them in between the antibiotics they might have a bit of time to work, but then most of them will get killed off by your next antibiotic dose.
Taking a probiotic after you finish the course would be beneficial in restoring your gut flora.

I don't know that probiotics would be of help but Xifaxan is quite specific to the intestinal tract exclusively and is not absorbed into the blood stream so you should not be in any increased danger of any unusual infections while taking it. Having said that, I don't actually know why you are taking it.

PS. just because I don't believe in the benefits of probiotics does not mean you should not take them if you feel them to be beneficial. I have no evidence either way.