Since I went to reg eagle redoubt and killed its leader BEFORE going to Markarth and trying to purchase a home there, The leader at Red Eagle Redoubt becomes bugged, never respawns back to life for me to kill him, and, for some reason, appears to be duplicating reg eagle swords. Bethesda, please take note of this...

You only have to help 5 people before buying the house. There is a lot of sub-missions in Markarth other than this one dude. Just keep doing them. Or join the stormcloacks and let the Silver-Bloods sell you a house

I think you have to be over level 20 as well.

In all my characters I have never been able to buy the house until the Jarl gives me a certain quest at level 20.

I don't think you actually need to be in a level to be able to buy the house. Skyrim isn't really like that. You just have to do a certain number of things and then you get the house.

Yes you have to be level 20.

You can do every single quest in markarth but you will not get the option to buy the house until level 20.

That is because the Jarl needs you to do a certain quest for him before he will allow you to buy the house. He doesn't offer that quest until level 20.

oh okay i didn't know. Still is really easy to reach level 20