For your first question, it actually depends on where you want to be a mechanic. Maybe some place like Ferrari, Mercedes, and/or Fisker are looking for a BA in Mechanical Engineering for their mechanics. But to be honest, most placed won't really care one way or the other because it's not as important to them as ASE Certifications, Manufacturer Specific Certifications (if you're looking at dealers or specialty shops), and years of experience. That being said, don't let that discourage you at all, because that's a very useful skillset to have regardless if it helps you get hired, not to mention you may find work that isn't exactly "mechanic's work." For example a while back I wanted a position as a vehicle test technician at Tesla, I'd work sort of as a mechanic with engineers to build, test, disassemble, ect. designs and components to design/build better parts/vehicles.
As for your second question, you have to realize that there is two ways a mechanic is paid. The first being Flat Rate (also known as "piece-meal"), this is the most common way to charge a customer and pay a mechanic because it is theoretically the "fairest" way to value job. The basic idea is that on average it should take a mechanic lets say a 1hr to replace an alternator on a Corolla, some days the mechanic gets it done in 30minutes and other days he's stuck on it for 1.5hrs. But it wouldn't be fair to pay the mechanic less wages because he's efficient and quick, or to charge a customer extra because he's being slow that day. So instead they look at the "Flate Rate" manual and determine that the job is valued at 1hr of labor and the customer is charged accordingly. This way the customer and technician are guaranteed a consistent cost/wage for any given job and it's not easily manipulated to fleece the customer or mechanic (it does happen and we can go into the politics of it later if you want a more "real world" explanation.) So basically if I do 8 Corolla alternators in one day at 30minutes each I've made 8hrs of pay in only 4hrs, this is why you may hear some mechanics say "I get paid like $50 an hour!" The reality is that they are probably paid $30 per hour, but their efficiency in the flat rate system is so good they are making more than 8hrs a day (but on slow days it hurts you pretty hard because you're not making your full wage; so this system is better for busy shops.)
The second method is simply paying the mechanic a flat hourly wage. Theoretically this creates a "better" mechanic because they are not constrained by trying to rush the job within the Flat Rate to make hours. The mechanic is paid a fair sum and can take a reasonable amount of time to do the job the correct way with much less pressure. The customer is still charged from the Flat Rate manual for the value of the work (unless some special things to be addressed, like let's say a custom port & polish job, ect.) This is typically seen in "higher end" shops that work on custom vehicles and so on because they want to focus more on detail than volume.
So those are the two theoretical/real world ways mechanics get paid (I'm not aware of any mechanics except for maybe Union/Government/Fleet Mechanics that get paid Salary, but I only have heard of one Fleet shop that did that.) Now on to what you mean by a "fair mechanic."
You need to realize that as a mechanic you are going to be underpaid for most intents and purposes in the general automotive repair field. A shop/dealer may charge $150 per hour, but you will only see maybe $30 out of that 1hr of work if you're lucky depending on which pay scale you're on (I'll be honest $30/hr is really high for most places), out of that $150 there's environmental fees & overhead to cover, and of course the service writer's commission (most are paid on a commission basis) and finally profit for the dealer.
If you're running you're own shop you'll find that while it's maybe not a bad thing to waive that $150/hr diagnostic fee for a simple fuse every once in a blue moon. You do need to pay the bills, equipment in this line of work is not cheap. As a mechanic you're talking easily $10k for a general assortment of quality tools and a toolbox (Matco, Mac, Snap-On, ect.) As a shop owner, you're talking even more money; for example last I checked I believe the TIS Techstream 2.0 (the full scantool with base and software) is $8k, not including the something like $1500 per year subscription to keep your TIS software license and access to the TIS repair network for software updates and so on. Then you need at least a 4-Channel DSO (Digital Oscilloscope) for modern vehicles, if you are not using one on modern CAN vehicles for your diagnostics, you're going to fall behind fast. The PicoScope is the typical "go to" brand and just the base kit with 4-Channel box and leads can hit $5k not including a laptop to run it on; plus the more complex additions you may want to add. So now as a shop owner you're easily in $100k or more in shop equipment, lifts, machines, ect. that you need to pay off before your company even turns a profit. Makes not charging that $150/hr for that fuse a bit more difficult to justify (again there's a lot more to consider as well, such as giving this "freebie" may establish them as a loyal customer, ect. but we're not getting into that yet) when you need to pay the mechanic for his time and cover the cost of the shop.
~
I think I'll stop there because I don't want to overload you with too much information or delve into the "workings" of the automotive trade as you haven't gotten that far in your questions yet.
I will mention that while I am a Dealership Mechanic (who is paid flat rate), that doesn't mean you can't be a "fair mechanic" within that system. I do do my best to fist a customer's vehicle to the best of my abilities and to my standard of quality (despite it usually meaning I don't make "hours" like my coworkers) and I do often try my best educate and explain things to customers if they have questions so they are given all the information to make a decision. I have advised service writers in the past to maybe not charge a customer the full diagnostic fee or anything at all for a simple "blown fuse" (at the cost of me losing that billable time off my own paycheck) because I would not feel comfortable treating a customer like that. While the politics and realities of being a Dealer Mechanic are not always "fair" or skirt around that ethical grey area. I still strive to do what I believe is the right thing or what I would do on my own vehicle; as that usually ends up being a good ethical code to live by. Basically if you focus more on striving to be a "fair mechanic" you'll end up being one despite wherever you end up, customers and employers may notice that and in some cases you may even get offers from others to be part of a "better" environment.
Post Note-
[MENTION=113771]AudiTech[/MENTION] got his post in before mine, but he's right. It's not easy to just label someone a "Fair" or "Good" Mechanic, because the industry does not breed these qualities let alone care about them. You can be a "Good" or "Fair" mechanic, but depending on which side of the coin you're on it can easily be a "Bad/Inefficient/Non-Profitable" or "Foolish/Naive/Easily Manipulated" Mechanic. The industry has gone in a direction that makes a black & white distinction like "good/bad" mechanic a more grey area. That's mainly why I said you should focus more on maintaining your personal standard of quality and ethics and trying to find a place that can accommodate those qualities and not try and not the other way around. You'll either be recognized and rewarded or you'll be punished and beaten down (in which case that place of employment no longer lines up with your ethical views and you should probably move on to a better shop in my opinion.) So I guess in the end being your idea of a "Fair Mechanic" means having a strong Will and core values, which isn't at all a bad thing.
(The "Flat Rate Mentality" is part of the reason I had to have my finger tip reattached a little over a month ago!

)