So everything I am listing here is either my personal experience( with DARs and all that stuff) or part of the research I have done for my own sake. Take all of this with a grain of salt because I may be wrong or not quite right and hopefully some one AD can correct me if I am wrong so I will have the info as well! I am just a fellow loud mouth depper as well!
1) Yes you can automatically sign as a CTN if you have a qualifying ASVAB score. Unlike CTI you don't have to take an additional tests or sign as a different rate and hope you qualify! yay for that.
2) When you have free time you can travel but if you have a security clearance you have to abide by a list of places that are considered off limits. I can't seem to find the link to this! ha oh well I am sure if you googled it you would find it!
3) Navy wide the average seems to be that you can start taking classes anywhere from 6 months to a year and a half after you get to your first command. It seems to all depends on your command and when you get your basic quals out of the way.
4) I am going in as a CTI and I was wondering the same thing because it seems like it would be so easy to do this. In fact for CTIs at least your language training only makes you proficient and not professional level which is what the ABC agencies want. Which lead me to look in to analyst positions which with a security clearance seems to be easy but you are going against people who are fresh out of college and its competitive as well as alot of people don't leave those cushy jobs! ha hopefully that made sense and helped a bit!
5) Any CT rate would be an awesome advantage for you. CTI will always be the one I say go for though! ha its because its what interests me. CTR was my fall back but wasn't available at MEPS. Definitely research about 6 or 7 ratings that will interest you because the Navy has a crap ton of applicants right now and you may only get offered 3 or 4 rates that you hadn't even considered (this happened to me since I had to sign for another contract before I could try to qualify for CTI). Be open minded and keep in mind that you can sign for something that interests you even if its not CTN then you have your recruiter submit a DAR for you to try and get you a CTN position if someone drops from DEP or some how one pops open for your MEPS station. If you do this keep on your recruiter because they have to resubmit it every month!
Hope this helped and good luck!