Here's my nickle's worth... hi..
For:
Question 1: No. In most cases the repeater will be open to all licensed amateurs. Some clubs/organizations do maintain closed repeaters but they usually have announcements along with the repeater ID stating that it's closed. Most aren't, I'd say over 90% are open. So once you're licensed just get on there when you're free and give your callsign out and say you're monitoring.
Question 2: Listen to the net a few times before joining in so that you learn their process. Most structured nets will always welcome non-member check in's but the NCS (net control station) has a specific time during the net which they will ask for non-members. So just listen for a couple of nets to get the process down. When they call for non-member stations or stations wishing to join, clearly state your callsign but nothing else (unless the NCS gives directions for more) the NCS will come back to you in the order in which they heard you and get more information about you and give you a chance to make a statement.
Question 3: The best way to get into the hobby is to go to a local club meeting. Meetings are almost all the time open to guests, and very welcomed. DON'T transmit on a repeater until you're licensed. Your question makes it sound as if you're asking if it would be cool to just get on the repeater and talk with other hams, don't do any TXing until you're licensed and have your callsign assigned.
I have a list of all the Clubs within a 20 mile radius of zipcode 43085 there are plenty to pick and choose from and it looks like most of them are geared to helping newbies out. Just look through the list and contact the clubs you're interested in first to make sure their meeting time/dates/locations haven't changed.
CLUBS Near Worthington, OH
I'm sure someone at any of those can help you with studying material, and help with where and when to take your exams. Some clubs might also offer study sessions like my club.
Good luck.