As with any app: look at the permissions it requests and think about whether the app legitimately needs those permissions. There's nothing inherently unsafe about using a custom launcher, but if it requests permissions that shouldn't be needed just to display a home screen, it may have hidden malicious functionality. (Or it may use them for legitimate purposes: for example, some popular launchers request permission to "directly call phone numbers" so that they can provide the ability to put direct-dial icons on your home screen.)
To see the permissions of an app you've already installed, go to Settings -> Apps, find the app, and scroll down to the bottom of its info page. You can also see an app's permissions in the Play store before you install it: scroll down to the bottom of the app's page in the Play store and tap on "Permission details".
Note that a launcher app will (naturally) know which other apps you launch with it. That's generally not a problem, but if the launcher app has Internet permission, it could potentially send information about which apps you use to a third party, which would be a privacy violation.
When you uninstall an app, any data stored with the app itself is removed; this generally includes things like customization settings. But if the app has "modify USB storage" permission, it may have also created files in your phone's shared storage area — the files you see when you plug the phone into your computer with a USB cable. Those aren't deleted when you uninstall an app, but you can delete them yourself, either with a USB connection or a file-manager app on the phone itself.
A custom launcher doesn't "override the native OS" in any unsafe way. It's really just a normal app that happens to respond to the phone's Home button.