It sounds like your dad has taken the first step of filling out the form in the Safari newspaper and picking what trails to do on which days. The Red Rock 4-Wheelers (RR4W) will put together everyones preferences and then go through a "lottery" process the first part of March to decide who is going on what trails. I have always got my first choices, but I have heard of others who haven't.
About mid March you will receive a confirmation letter from RR4W, explaining which trails you are signed up for. Take that letter with you to Moab and take it to the registration desk at the Arena. There you will receive your packet which has your raffle ticket in it and some other stuff. They will also tell you where your trails will be departing from (this information is also in the newspaper). If you signed up for a trail on the Saturday before Easter (Big Saturday) the trail will leave from Main Street as part of the "parade".
I know all that sounds complicated, but its not.
The key to having fun at Jeep Safari is to relax, not take anything too serious, and have fun.
As far as hotels go. Many of them are probably already full for Easter weekend, but there are probably plenty of rooms for the other days. Many hotels have waiting lists that you can get on and as people cancel they will call you (I've gone this route before and ended up with a room). Hope some of that answered your questions.