There are two types of groups. Most are open to anyone who wants to comment or join/add. Only a few are members only, where you have to ask to join. And it's important to know that if you ask and don't get a reply, that doesn't mean they read your request and decided not to let you in. It's much more likely that the group isn't active anymore or the leaders have dropped out.
And "friending" here is very different from Facebook and similar sites. Here, adding someone as a friend doesn't affect them in any way. They probably won't even know you've added them unless you leave a comment on their page. Adding someone as a friend just makes it easier for you to find them again, and you get some of their activities in your "Friend feed" on the right hand side of the page. It's really more like bookmarking than like Facebook friending, and it doesn't have to be mutual.