Others will probably give more complete answers, but here's my best try:
1: The Against the Bot Campaign is a special set of random scenario and opposing force generators that allow you to run a campaign against the bot as per
http://bg.battletech.com/forums/megamek-games/campaign-rules-against-the-bot-thread-4/60/Without those rules, MekHQ isn't nothing but a very nice(!) record keeping tool for campaigns.
2: It depends on what you want. Some use MekHQ to keep track of their table top campaign forces, others make their own contracts and scenarios, and then there are the Against the Bot rules (see link above).
3: The Against the Bot rules create random contracts for you, otherwise you'll have to manually obtain and enter all values.
4: Under campaign rules there should be an option of how to calculate the rating: either 'Interstella Ops Beta' or 'Field Manual Mercenaries: Revised'. The first is the default one and gives a numerical rating, the second is an older one that gives a letter rating (with a numerical value in brackets, though it won't match up with the IntStel OPs calculations).
As far as I can tell, the default method gives you lower ratings mostly because it requires a lot more administrative personell.
5: It stands for Margin Of Success, ie how many points you rolled above the target number. The higher the roll, the more potent the effect, usually.
6: General opinion appears to be that the maintenance rules were written by someone who didn't think through their implications for long term play. Yes, maintaining a mech is apparently a task requiring a veteran or better to not botch frequently. There is an opportunity to fiddle with the settings to make maintenance easier. I just turn maintenance off but keep assigning techs anyway, just pretending that they're doing their job. Battle damage usually gives them enough to do/fail at anyway.
7: When doing customisations, keep an eye on the time/money/refit class needed. The more complex the refit, the more time it will take and the more difficult the roll will be. Modifications only get one roll: pass at the end of the time and you're done, fail and it will take double time.
Changing structure, engines and/or Case are the worst offenders for driving up the time and target numbers.
(And a note: If you have a mixed IS/Clan tech mech and want to modify it further, meklab tends to switch the armour type to Clan Standard by default, regardless of what the mech had; if you don't set that back where it's supposed to be, you're in for a super long refit).
8: The temp ones are fine and will keep your personell list and save files smaller (helping performance). If you're playing Against the Bot rules, you'll be swimming in astechs soon either way, though.
9: Table of Organisation Equipment, I think. Basically anything in there is considered to be an active, deployable part of your unit. When an employer asks what you can bring to a fight, that's what you show them (ie contract payment is based on that).
10: Sorry, I don't know. The batch I got from the megamek forums uses 150*150 png files, though the default is a 72*72 gif. I think as long as they are in a folder called either 'male' or 'female' in data/images/portraits/ they might work?
11: I don't think anything happens at the end of the contract. After each scenario you get your pick (or a payment if the terms were 'exchange'). To total for both sides is tracked, so if you go over, you can't get any more salvage in future scenarios of the same contract until you've collected enough to go under your share again. That means you can grab as much as you can get away with in the last mission if you want, if that's how you want to play? Can't imagine the employer being too happy, but it's your game (that is the most important part about MekHQ, btw. It's your game.)
12: The idea is that if you don't have jump/dropships, the employer will get you to your contract destination somehow. MekHQ tracks payment per jump if you don't have 100% transport capacity, but I believe those rules are officially referred as 'a hack' for now because there are no official guidelines just yet. Note that if your contract has 100% transport costs covered by the employer, you won't pay either way.
13: Not really. What you can do is GM-> remove the unit to be refitted and purchase -> Add (GM) the unit you wished to refit it to (you may have to set your available tech limits in the campaign rules and probably allow non-canon units for purchase to find them, though).