In general, 3k–8k pace. There's all kinds of sessions you can run. A classic is 12–16x400 with 60 seconds rest. Start off slightly slower than 5k pace, finish a bit faster. You might do 4–5x1600m @ 8k pace with 2 minute rest, or 3x1600 @ 5k pace with 3 minutes rest. You can even do multi-pace sessions. I like stuff like 5x600-200. Run the 600 around 3k pace, maybe a touch slower, take 30–45 seconds, run a 200 at about mile pace, 2–4 minutes between sets.
That's fine, 5,000m is probably better. If you're really training like an MD guy, 10,000m will be absolute torture, but you could do an early season 5,000m
Squats and bulgarians are great, I do them all the time. Jumps are great too. But it sounds like you need some periodization and more variations. You can't do the same thing all the time, you plateau. You have to mix it up in phases. I would try to find a coach if you could. If you can't do that, start Googling. One of my favorite books is "Functional Training for Athletes at All Levels: Workouts for Agility, Speed and Power", it's a good primer on how athletes should train.
Weights will do that to you. A good piece of advice is keep your hard days hard, and your easy days easy. That means when you do your hard running, do your lifting later in the day. That way, the next day when you're feeling like sh*t, all you have to do is slog out a recovery jog and some easy strides. This goes back to periodization as well, it's okay to be sore and tired, but it's not okay to be too sore and too tired. Once you're approaching your peak, your weight training should be minimal and not causing too much fatigue, or any at all.