Unless it is an emergency or your job requires it, cell phones should be silenced and not answered during service, JMHO. Texting and all that is unnecessary and disrespectful. Answering a call, take it to the foyer/nave/outside.
I'm shocked to hear that a priest would have a cell phone go off, be answered, and especially talked on during someone's confession!
Babies crying: even Christ said to forbid them not...I would rather have babes in the service and exposed to the same Grace as everyone else. If the child is just wailing loose, sure take them out and settle them, but to not have Grace for the parent is a bit absurd.