This is not just normal behaviour. It is the start of falling for someone. Not everyone searches everyone on Facebook. If I search someone it's only if I have a strong interest in them. I would never give my personal mobile number out to a colleague even for safety reasons (unless I am attracted to them sexually) the safety thing sounfs a bit like an excuse to me. Would he have given his number to an ugly colleague for safety reasons or a male colleague?
He probably wouldn't cheat. But he might be falling for her , there's nothing wrong with that, he probably doesnt even realise it himself yet, but once a guy falls for someone else There is absolutely nothing you can do to get them back. I would monitor the situation. It seems this behaviour Is very out of character for him which is where the concerns come from. If he always gave work colleagues his number, checked them out on Facebook etc it wouldn't be such a deal.
He might have told her he had a fiancée before he became interested.
It's absolutely not paranoid to be suspicious. You'd have to be a right walk over to have no concerns about this.