Do +1/+1 counters accumulate?
Yes it can. Every instance if lifegain grants another +1/+1 counter. So if you play 10 Swamps, you have 10 instances of lifegain, which grants 10 +1/+1 counters. If you have a creature with lifelink which deals damage, you gain life, so Ajani's Pridemate gets a +1/+1 counter. There is no limit to the amount of +1/+1 counters it can get.