Power play (PP) is like Risk, the board game, but it isn't separate like cqc, it's played out in the galaxy we all share (but it's totally optional). You pledge to a power and help it fight over territory with other powers. You get different perks for pledging and gaining ranks, by helping (your rank needs to be maintained).
It's split into weekly cycles (like game turns) which start Thursday.
PP adds perks to players even if they don't take part. For example, one power provides an outfitting discount in any station that it controls.
You can Google Elite dangerous Powerplay guide for more details. I find it quite fun to take part in and each power has a sub forum where the players discuss strategy. It's really very well organised by the players who are into it. If you have time to invest in PP, you get the most out of it by reading the strategy discussions and really taking part. Otherwise, you can still benefit by taking part (for example Hudson, my power, gives up to 50% extra bounty claims in Hudson controlled space, just for maintaining 100 merits, which is easy).
But, as I said above, it's totally optional. You can largely ignore it if you don't think it sounds fun.
You don't need to buy horizons, you're a premium beta backer, so you get all expansions for free.
Horizons is an expansion that provides you the ability to land on airless, rocky or ice planets. It adds the SRV (surface reconnaissance vehicle) and some new content that is still being developed. I won't go into details but buying horizons gives you a "season pass". Basically, it means you get the usual free updates through the next year.
You don't need to buy it. You can continue to play without it just fine. But it is the same game, just opens up more content.
It is stand alone in terms of buying it. If you buy horizons you do not need to also buy Elite dangerous. It includes the base game.
No idea if that will continue in future but I don't see why it wouldn't.
I recommend reading up before you buy.
