That is a coaxial port. It’ll work for TV or internet, but not without some extra hardware. This will work to plug in your incoming cable/satellite TV to your set top box, or from your ISP to your modem if you’ve got cable internet. Generally, cable TV/internet will come in to your basement/furnace room and then ran from there to other places in the house. You can use this for ethernet using some extra hardware which is called MoCA. You would have to find out where the other end of this goes first before you can make any use of it. Most often these are used for TV though. Cable TV if you’re in a city and satellite TV if you’re in the country.
I got a new battery in my 2015 MacBook at an Apple store about six months ago. Cost about $300 CAD everything included.