In answer to a supplemental question, if you have enemy armies on your land (enemy meaning you are already at war with them) it appears safe to chase them off. The Pope lets you defend yourself. Attacking them on their own turf is a no-no. I have never observed a drop in relations with the Pope for doing so. On the other hand, naval attacks count as attacking the enemy on HIS turf.

You've already gotten the advice to play the Pope-o-meter slots. I usually race my starting dip or pricness to Rome, set up a slush fund, and then I get a fairly free hand. Keep an eye on the meter. If it's below 9, hold off agressive acts into lands not yours. 10 is close to completely safe. 9 is mostly safe. Below that the odds rise, but relative standing is still important, so watch the meter for both yourself and your enemy.

I usually start with 100 for 20 turns. Early, as early as I can get over there, that's plenty. Later, the amount required goes up. If I live farther away, I sometimes set up a longer fund to keep something going in case it's hard to get back. Once I can, I park a dip in Italy. I never bother giving the Pope land. It just makes him aggressive. He's already a pain in the meter.