I pump exclusively and when I first switched to it, the baby would spit up a lot. It just took a few days for him to get used to having a bottle and then it was no problem.
As for the little cries, if he's asleep, just let him be. My LO is older than yours but he'll let out a little yell in the night sometimes and he's totally asleep. it's nothing to worry about. If he was in pain or hungry, he would really cry and wake up.