1. Starting Warehouse is determined based on starting faction for the purposes of contacts, well-connected, etc, correct?
I don't understand the question. Starting Warehouse what? Money? Parts?
2. Do the number of acquisition rolls match the starting timeframe? So, I've got 4 months worth of money, I get 4 months worth of acquisition rolls to fill my warehouse? I understand max rolls per month is controlled by WIL or CHA.
Starting characters need make no acquisition rolls. You can spend your starting money (which is the base amount + 4 months worth) as you see fit on IntroTech gear.
3. When looking to acquire personnel - such as a doctor, what list do I use? I would not expect the unit's list until after I'm officially part of the unit between contract end/beginning.
Lances don't start with doctors; to hire one, you'll look in the Marketplace topic posted on this forum, and choose a doctor to hire. Originally, Doctors were a "whole unit"-level asset, but that proves too much of a PITA to track, so the existing unit doctors were split up randomly between lance members (and a few lances, like mine, had to hire them from the marketplace).
4. I've been looking for salaries for personnel. I found some listed in Paul's lance creation thread. I did not find them in the rules, Tac Ops, Strat Ops or TW. The salaries in AToW don't seem to match. The salaries I'm missing from my chart are WM - Enlisted Green & Elite, Doctor - Green, Regular and Elite and MW - Officer Elite. Can someone fill in the gaps? For my PC who's 4/4, he would count as Regular until I get the Gunnery to a 3, correct?
The AtB program uses almost all the stats from Field Manual Mercenaries (Revised). Look on page 148.
5. Is there a good rule of thumb on number of months worth of operating costs and hiring bonus money to keep in reserve? I'm not sure how frequently the lances get paid and am trying to figure out how much of my starting cash to spend on parts and how much to hold onto.
Not particularly. The campaign has been too new to really grok that. Lances get paid every month while they're on a contract, and you get your Trait-based money every month whether you're in a contract or not.
6. Along those lines, any rules of thumb for excess tech capacity above maintenance requirements to ensure time for repairs and refits?
You will generally want ~4-6 Techs. You'll want them roughly evenly distributed between Green, Regular, Vet, and Elite; if you miss a repair roll, you have to re-try with a Tech of a HIGHER skill level to affect that repair - if you don't have a Tech of that level, then the repair is impossible barring some major exceptions (ie, tear all the armor off the location, trash said armor, and put totally new armor on that location). Note that even the vet players don't have full sets of Techs yet; Elite Techs are VANISHINGLY rare.
7. Looking at the section "Force Tracking, C-Bills" am I correct in understanding that a lance must be able to cover all expenses BEFORE getting their income for traits and contract?
Technically yes. However, in practice, you aren't going to have to worry about it. Maintenance costs and salaries are ridiculously low compared to the values of Mech parts.
8. How are personnel's additional skills used?
Most of the time, they aren't. However, some scenario can call for them to be used (remember when you and Brent dismounted from your Mechs and fought your way through a bunker)? Some skills get used as a result of random events in campaign play. Gunnery on a Tech, for example, can come into play because it's entirely possible to end up with a scenario where your TECH is piloting a Mech (see the "Star League Cache" scenario thread). Most importantly, if your PC ever bites it, or is on the long-term injured list, you can use a Wingman to act as a replacement Lance Leader, so you can still have ratings in important things like Tactics, Strategy, and so forth. Some skills are only important for the Unit CO, in fairness (mostly administration) - but again, can be called for as a result of random campaign events.
9. How much does an engine cost? Formula for a standard engine is (5,000 * Engine Rating * Unit Tonnage)/75. Consider a 300 VLAR engine. It's the same engine that would go in a 100 Ton (3/5/0), a 75 Ton (4/6/0) a 60 Ton (5/8/0) a 50 Ton (6/9/0) or a 30 Ton (10/15). The price varies though from 600,000 for a 30 Ton Mech to 2,000,000 C-Bills for a 100 Ton mech. Is it really not possible to move the exact same rated engine from one mech tonnage to another?
No, you can't move an engine from one Mech to another of different weight. Yes, we know it's stupid. You have to specify the tonnage of engine you're buying and storing; look at how engines are listed in my Warehouse doc. Catalyst errata'd things to work this way a decade ago, specifically because players in C-bill campaigns were taking 30-ton Mech engines and shoving them into 100-ton Mechs.
10. What parts are considered in scope for Mech Quirks and need to be rolled for separately (Ubiquitous, Non-Standard Parts)?
If you're buying parts for a Mech with one of those quirks, that part needs to be separately accounted for. So you can have an "Upper Arm Actuator, 50 tons", and an "Upper Arm Actuator, Enforcer" listed separately in your Warehouse.
11. From the rules "Green begin at a TN 9+ (Skill Rank +0), and are not considered Regular until reaching 7+. For ease of use, the 8+ skill target will not be tracked; save XP until you have enough to reach Skill Rank +3." If +0 is a 9+ TN, wouldn't +3 then be a 6+ TN (Veteran)?
Typo. That should say "Skill Rank +1", not "Skill Rank +0". So if a PC came out of character creation with a Small Arms skill of +3, they would be have a Regular skill rating (7+) in Small Arms. This is an artifact of the Against the Bot program, and we're having to adapt to be able to use said program (otherwise all the contract $$ values will be wrong).
For what it's worth (because you're coming at this ruleset without context), our last campaign disintegrated, and this campaign ruleset was written from scratch in 3 days so we could play the following month after the previous campaign ended. We've had a few revisions since, but everyone's aware that strict RAW readings of the ruleset will make the whole thing fall apart. Because again, written in 3 days with no editing passes. Basically, as a guideline, if the bulk of the rules are intimating one thing, and a single word or number somewhere makes it work the opposite way, then go with the bulk of the rules.