Can I turn off Google services?

Go to Settings > Applications > All > Google Play Services > Tap Disable > Tap OK to confirm. Method 2. If you find the Disable checkbox is grayed out, please Go to Settings > Security > Device administrators > Disable Android Device Manager.

I have an app but I was thinking to just remove it also to free up space, would that help?

If you don’t want to use it anymore, yes you can remove it.