For a disc you need a new fork if it does not already have mounts for the disc calipers. By "new set of gears" I assume rear cassette. You will need a chain whip and a cassette tool. Keep in mind that all drivetrain parts tend to wear together. Its important to swap your chain when it starts to wear. I just do mine every spring to be safe. If it's been awhile, you'll need new chaingring(s), casette, and chain. After a longer time, it's good to replace the pulleys in the rear derailleur too.
But like others have said, with this amount of effort, just get another bike.
Bit late to the party so I don't have much to offer that hasn't been said already, except: if you don't want to buy a specialty tool like a chainwhip you can jury rig it with an old chain and a pipe wrench or similar to clamp them together - just gotta stop the gears from turning
Just be reaaaaaaaaal careful and think about how you're applying force and which way your hand goes if you slip, I've got a scar from slicing my hand open on the sprockets lol
Depending on your location if you want better front brake than normal V-Brake or maybe Cantis, Magura makes hydraulic rim brakes and they just slot on the existing infrastructure. I can find them here for about 20€ / brake on the craigslist equivalent, but then this is germany where they hail from. Also depending on location maybe there's something like a self help repair workshop or a bike kitchen near you that could help you out.
One last tip that helped me greatly in all things bike maintenance is to spend a bit of time understanding how it works. Sure you can follow a set of directions, but especially for say, rear derailleur adjustment it's a much easier time if you actually understand what the fuck the H and L screws do and why to troubleshoot any mistakes. Most guides presuppose you're wrenching on showroom floor type bikes, hardly the case in the real world.
Park tool has good, informative videos: park tool
Saint Sheldon Brown is one of the best, original sources for internet cycling knowledge.
You can, but it often requires either welding on a bracket or swapping the entire fork. At that point, just get a better bike. Even walmart bikes have discs these days.
Not really, just personal experience. I would go on youtube for it. Youd have to figure out what kind of gearset you have, which you can also use youtube for.