Download (from the USCIS site) and read the Guide to Naturalization. Almost all of your questions will be answered.
In general, if you are 5 years after your GC you are eligible to apply. You can actually apply 90 days before your GC's fifth birthday.
Can you leave the country, for 1-2 months? Maybe. There are two main rules you need to respect, "continuous residence" (a two month vacation will likely not affect that) and "physical presence" (if you have traveled a lot, and extra 2 months might bite you).
But, you will be told to get your fingerprints done fairly quickly after you apply, so don't travel before that. Depending one your office, they may be processing things fast enough that there is no 1-2 month period where you can be assured they will not ask you to show up somewhere (and, missing appointments can lead to long delays).
How long will it take? Good question. It's taking between about 3 months and 3 years right now, with typical applications in the 5-8 month range. Figure out what district office you would be interviewed on, and then check out the "timeline" thread for that office.
Good luck
