AnilApplelinkB

Usually at least at newer buildings I have seen these are housed in a box like the one on the left. Most likely the one on the left is for cable.

It requires power to the adapter so yes it does require one

Good RG6 Coax cable with compression ends are really resilient to weather. Even crimp ends are pretty resilient. Unless the ends look really corroded they might be fine. There may be Non-MoCA compatible splitters within the home. How many coax connections are there throughout the house? It might be worth it to buy a cheap cable toner/tester although they dont always work too great with Coax it may help find your cables and if they run to the outside location. Below is one that will work with the Red and Black clips included. You just strip a piece of coax with a connector on one end and attached one to the center copper and the other to the shield. It will still tone through splitters though but at least you will have a better understanding of if the wires you tested before are connected somehow to the outside.

https://www.amazon.com/Fashionwu-Multifunction-Collation-Telephone-Continuity/dp/B0B4WN1YNL/ref=sr_1_10?keywords=Cable+toner+tester&qid=1699939189&sr=8-10