How many openings ?

For long-term improvements, Is it better to play several openings, just a few, or stick with a single one ?

Stick with a few, understand them, then move onto another opening.

You can't improve if you stick with only one...remember you will also play as black...but you need to have a few for both black and white which you are comfortable with.

But it is ok to just stick with just one colour to write in.

You start out wide, to figure out which resulting middlegame positions you like the most, which concepts you like the most (attacking, sacrifices, maneouvers etc), and then for your serious games you'll have to eventually narrow it down. I would want 1 or 2 defenses as black for 1 d4, 1 e4 and maybe 1 c4 that I know really well, if you want some backups for suprise value that's up to you. For white of course you pick your first move, and then pick how you'll counter each black defense. Again 1 or 2 main choices is ideal.

If you're just having fun with it, you can of course play as many as you want, but you probably won't play many of them too well.