Running schedules/programmes?

you don't have to race to train for a race. I've trained for 6 marathons without running one. Ok, I had intended on running the races, but I didn't for a variety of non-running reasons.

Getting "faster" also often depends on how far you're running, too. You can train for a faster 5k, faster 10k, faster 200m dash... All of which have their own theoretical ideal "bases" (mileage you run when you're not training for a special race). Then improving your pace/speed requires a tailored training program for your intended distance. Most distances 5k and above involve at least one day of intervals, one day of a "pace" run (your goal pace but for a shorter distance), and one LSD (long, slow distance way farther and way slower than your goal). Fill in the rest of the days with "easy runs" that are aerobic or some kind of cross training or both. It sounds like you're already doing all that, just without a goal.

For every distance shy of a marathon, I use races to train, rather than train for the races. I'm not competitive, at any distance, either. For me, I found that training without a goal date and distance (i.e., race), I quickly get bored or lose focus. So I register for a race and make sure I'm in shape to finish with a time that I personally find respectable (though sometimes I shoot for PRs, but usually not - I'm too social with my races).

Oh, one other thing I've done and seen massive improvements in my running - swim. At one point I decided randomly to start swimming 3x a week for 30 minutes (nearly drowned the first few sessions, it's harder than it sounds for a noob like I was), and without changing my running schedule I dropped from an 8 minute mile 5k pace to a 7 minute mile 5k pace. Didn't lose weight, did't gain muscle. Just learned to breathe differently with an elevated heart rate.