Hi and welcome to the forums!
You're right, the AI can only send waves to a planet adjacent to a warp gate. However, if you kill every single warpgate on your borders, it will have to send waves to its own planets, which will then travel to your territory through wormholes and attack you wherever they decide to. This makes dealing with waves much more difficult, so it's better to leave some warpgates on your bordering worlds. If you only leave one, you will pretty much always know where the waves hit and heavily reinforce that system with turrets, but that is the extent of what you can do. You can't stop the waves completely.
There are also other things that function as warp gates, AI Eyes and Warp Gate Guardians among them. When looking at a system, you can see the number of wave-capable warp gates in the top left.
And yes, if the system has a IV next to it on the galaxy map, it's a mark IV system. Do not disturb without good reason