1. Can I buy a up to date replacement and just pop it in the same socket? If so What is a good replacement (Yes Im playing Doom eternal as well)
Actually yes you can, well...sort of. Technically since you're on the AM3+ socket you can mostly likely upgrade to a "newer" processor such as the FX series, which supports SSE3 and would solve your problem (check what your motherboard supports, and it may or may not need a bios update for the new processor to work).
However, I said "sort of" because no one in their right mind here would recommend Bulldozer or Piledriver CPUs over a new build because they have such a bad reputation. But it would solve your problem instead of having to get a new motherboard/ram and deal with migrating the OS and all that.
You could get an FX-6300 for about $50 on ebay. This "6 core" processor would perform about the same in games as your current quad core phenom (See the problem here?) but it and will run Apex/Doom Eternal and might run certain games better solely due to it supporting newer instruction sets. All you'd need to do is swap it out with your current processor and problem solved.
Last option would be to get the 8 core versions such as an FX-8320 or FX-8350. An 8320 will run you about $120 on ebay from a US seller and would be close to the most power you can get out of your motherboard.
As terrible as a reputation as these processors have, the latest revisions (piledriver) aren't THAT bad for gaming (and they're cheap because no one wants them) Since more games are using more than 2-4 threads as opposed to when these came out they get better utilized. And based on benchmarks the single core performance of Piledrivers aren't lower than your current Phenom...So it won't be any worse.
Just something to think about if you haven't already bought parts.