If someone had a WR on here for a long time, but was found out to be cheating via manipulated code, and that run was then removed, would you ever accept a run by them for that same game? Even if it was legit?

The answer to that is going to differ by game, community, moderators, and circumstances. It can be tough to tell when former cheaters reform, but it does happen. Some communities ban certain runners who have committed too many "crimes."

I understand that. I decided to remove my WR time from Speedrun.com. The moderator has never run the game more than 30 mins and I myself am not going to watch a cheaters 3+ hour run, (was never given moderator) to look for issues, when I was the person who discovered his first WR run (posted for over a year) was on a manipulated rom. This game only had 4 or 5 runners ever.

Considering how easy it is to cheat runs, no.

I guess there should be separate categories. As in, you put a [Clean] tag in your video description if you're not cheating, and a [Cheat] one if you do. Also it depends on the level of overpowered-ness allowed by the cheat code. Something like infinite money in GTA is A-okay as you still have to fight, do the quests etc, but something like invincibility in a FPS just removes any sort of challenge.

Generally no

If a player is a repeat offender of intentionally cheating, modifying, TASing, or otherwise using illegal methods of speedrunning a game, they shouldn't be allowed within the community, possibly the entire site. In the case of some communities, they will enforce rules that either make No Emulation Rules, make Emulation in its own category, or higher attention to players doing well on Emulators. Even outside of that, high ranked players will be investigated before being concluded as a valid player. The site as a whole will often ban users attempting to get away with cheating for extended periods of time, and/or repeated occasions.