samsung galaxy j3 - Problems with Google Play Services

I am using a Samsung J3. I suddenly have problems with Google Play Services, with the message that unfortunately, it stopped. I took the following steps:

1. In apps, I forced stop, cleared cache and restarted but didn't work


2. Then I uninstalled Google Play Services with a view to reinstalling


3. I wasn't able to reinstall from the phone itself, so I turned on the option to install from other sources and installed it from the internet


4. However, it's not in my list of apps now, even though I think it was installed.

So basically when I try to open Google Play Store, no reaction. When I try to open Play Music, YouTube, Gmail, maps etc, I get the message to update, but pressing on update just brings me back to main screen.

Any ideas?