When I do pass, how do I apply for a callsign? And how does my license come- "paper or plastic?!?!?!?!"
When you pass all the required elements for a license, you're given a callsign from the standard callsign pool based on your license's mailing address. Once you receive your callsign, you may apply for an appropriate vanity callsign if desired.
To practice, I use:
eHam.net Ham Radio Practice Exams but don't know of any sites to study on. (I'd like a FREE one)
Your local library probably has a copy of the ARRL or other group's study guide. Just make sure it's current since the question pool change every few years. What's nice about these types of study guides are instead of teaching you the test, they teach you the material so you'll have a better grip on the material. Instead of just learning that the answer to question 4 is "B", you'll be able to answer the same question even if they rearrange the answers to make the correct one "D" instead.
Another good way to study is to find a local ham radio club that has classes you can take. These are often free (although you may need to purchase the book they base their class on) if you join the club. Another advantage is you get to study with others and can bounce questions of eachother. These folks will make good on-air buddies as well when you get your license since they're new as well!
What is the best (cheapest) radio to have. I'd like to get a portable first- then a mobile.
In reality the cheapest radio is one you don't have to pay for (and a few are out there legally). One way is to join a local club and use their equipment. The downside is that you'll have to go to the clubhouse to operate. You may also find a local ham to "elmer" you (help you through the process of getting into ham radio) who may have an old radio you can borrow once you get your license.
There are also many used radios that may allow you to find a much better radio than you could afford new. The advantage is you get to learn how it works and sell it for about what you paid when you want to upgrade (making it nearly free to use).
When you get a frequency, do you own it, or sort-of rent it? Obviously I realize that people can scan/ monitor it.
Your ham license doesn't grant you a frequency, but allow you to use the many frequencies allowed by your ham license grade based on the approved bandplan. These frequencies are shared by all hams with rights to them. Some groups may have a bit more "rights" to specific frequencies, however this is very limited.
One example would be a repeater frequency assigned for an area by that area's assigned coordinator. While it may be legal to use either their input or output frequency for your simplex conversation, it wouldn't be well received by others that use that repeater.