New person with several questions

[Broken_Arrow]

1. Is there a method to find which US server/data center will be more active at night. Since I work the long night shift I am more likely to be playing at the late hours.

Currently not that I know of.

2. What is the leveling curve like for inexperienced players? Would I expect to be level capped on one class (which I believe to be 50) within say 2-3 months?

Depends on how often you play, how devoted you are to a single class (or just getting your sub class to 15 to get a job class). I played for about 2 weeks and I'm level 36. I also have a pugilist at level 15 and a carpenter at level 15. You should be able to do it in a month.

3. Does it work better to lvl cap one adventure class then work on another or simple work on the ones that are interesting at about the same rate. For example get my lancer up to 20 then pick up archer and work him up to 20 before moving back to lancer.

I would suggest work on the ones your interested and their sub-class for a job. Once you max your main class/job, go for a crafting/mining job for gil and better equipment. This will give you an easier time later on, especially when more expansions are released.