Quoted:
I'm looking subsonic ammo to use for plinking, so I don't want to spend a lot of money. I will be shooting mostly in a RARR but later in a Sig MCX, so I'm also looking for ammo that will work in a semi-automatic.

I don't want ammo that is going to dirty up my rifles and suppressors, so if that means no polymer coated rounds, it'd be good to know now.

A coworker has a .300 BO and he said he used the subsonic Sig ammo but it was not actually subsonic and was supersonic. Don't know if he got a bad batch or what, but he said he won't use it anymore. He said it cycled fine.

1.)  Is remanufactured ammo bad?
It can be or it can be okay.  Depends on the manufacturer and the reputation they have.

2.)  Is loaded in once fired brass bad?
Largely this is just reaffirming that it is manufactured ammo.  Ammo can blow up your gun if its not correct, see 1.

3.) Is fully processed brass bad? (What does it even mean?)
Fully processed largely means, cleaned, resized, trimmed to length, chamfered, primer pocket cleaned and deswaged.  I'm sure I forgot something here someone can add.

4.)  Is polymer coated lead bullet bad?
It is a different process to load quality coated lead bullets.  Some folks say they dont cause them problems in their suppressor and others do.  I have no personal experience to share.

I'm assuming that if I order from a website that is on ammoseek that it's a reputable dealer and I won't have any problems, correct?
I order from SGAMMO largely, sometimes Midwayusa, Brownells, Natchez, MidSouth, Wideners, Grafs, Ammunitiontogo...  Best plan is to search to learn about the reputation of the specific vendor in question, but I have never had a bad deal with most of these folks to the left... Midway recently had a ammo SNAFU that is on everyones minds so some are avoiding midwayusa.

Some of the ammo for cheap I've found to be on www.ammoseek.com and I've seen these brands: Are these all good?
I have personally never heard of or used any of these except for S&B.  I have not used their 300 BLK ammo but their pistol ammo is okay.  I use remington subsonic if I do factory 300 blk.

https://www.peakperformanceammo.com/product/300-blackout-220gr-subsonic-3000ct/

https://www.tntmunitions.com/300-blk/bullet-150-gr-fmjbt-target-reman.html

https://www.venturamunitions.com/ventura-tactical-300-aac-blackout-147gr-fmj-ammo-250-rounds/

http://sgammo.com/product/300-aac-blackout-ammo/20-round-box-300-aac-blackout-147-grain-fmj-ammo-sellier-bellot-sb300b