With the proper adapter and cable you can connect the laptop to your TV.
You can try booting into Safe Mode to see if you still have the same issue since Safe Mode prevents third party drivers and even some Apple drivers from loading, and prevents Startup Items and Login items from launching. If the issue doesn't occur with Safe Mode, then you know you have some sort of software issue.
You can also perform a clean install of macOS to see if the issue occurs with just macOS and Apple apps. You can do this by installing to the internal drive if you first backup your data or to an external drive. A clean install is when you first erase the whole physical drive before installing the OS. You must test the computer before restoring from a backup and before installing any third party apps.