I just tried the FB app a few minutes ago and it did let me like a post without problems. But I really dislike the app. The posts and pics are huge. Many times the tops of photos are cut off since they are so large. And yep - I am new to Apple so it could be that there is something else I should try to improve that app.
Regarding the browser question - I will have to try others out again. I've only had the iPad for a couple of weeks and I tried those browsers in the first days. But it's a good question and I'll give them a try again.
Thanks very much.