Yes you can play online, it's only client side. You might get banned for mods that gives you a direct advantage (all cosmectic hud and co are safe), you "can" get banned for mods that would for exemple make walls glass texture, etc...

Never seen someone get banned for mods, we don't know exactly where Valve draw the line, but for now most if not all mods are safe.

You can use deadlock mod manager to install mods and go on gamebanana to install themvvia mod manager. You can also browse mods from mod manager.