1 and 2 are... not anything we can answer. Typicially speaking it'd probably be a bad sign if the other Warriors were ******** who won't give you the time of day, but the level of 'apprenticeship' or similar you might see is going to vary wildly. For that matter, the MT position tends to be fairly static; if there are other good, competant Warriors there they're probably filling the slot, but attrition and time off means you could get it eventually.
As for #2, the site will usually have an application template, with questions about yourself and your gear, or you may be recruited in-game (depends on the level of the guild; most of the larger guilds require formal apps, smaller ones tend to not). If there's an application, fill it out and don't lie; they don't tend to be horribly complicated. Use proper grammar and try not to go either way overboard on information (i.e. "Tell us about yourself" is meant for a paragraph at best, not a three-page answer) or be too terse ("What is your gaming experience" should probably not be answered by "Stuff"), but other than that it's... something you have to figure out on your own. Use common sense.
As for #3, it usually helps if they have an opening you can fill (offtank to start, most likely) and you mesh with their members, i.e. you don't find them horribly annoying or vice versa. Heroics aren't what most people consider end-game, though... more like middle-game. If you haven't run many (any) Heroics before, you're not likely to have much luck getting into even a decent Kara guild. Especially as a tank you can find a group for Heroics fairly easily; it's the best way to look for guilds and start making contacts.
As for #4, yes.