privacy

You can't uninstall Play services once it's installed (or if you're on a stock ROM where it's "baked in"), but you can disable it. Apps -> Set option to "show system" -> Google Play Services -> Disable

Will it crash as soon as I uninstall it?

No. However, you won't be able to use most Google apps and RCS messaging and anything that relies on Google sign in or integrated Google Maps will not work.

You'll also get hammered with "Google Play Services are unavailable" notifications from SO MANY APPS. Most of those, you can go into the app's notifications and disable the alert for "Play Services Availability". The only one I can't disable on my phone is from Android Setup, but it only pops up once after a reboot.

Some apps depend on it more than others. Some will just complain that Play Services aren't available but otherwise work just the same, but others will lose some functionality depending on how they use those services. For example, my bank app still works but complains Play Services isn't enabled.

Most apps that depend on Play Services use it for notifications. So, with my bank app, I no longer receive transaction notifications. I can live without those, though, but some people may not be able to.

Can I have Android but not Play Services?

Yes. Most custom ROMs don't include it by default or offer builds that exclude it.

Should I use MicroG? If yes, where do I download it?

You can only install MicroG or other Play Services features before booting into the phone for the first time (e.g. with custom ROMs), but you can't just replace Play Services with MicroG.