Garen Marethi asked me if I wanted to have the garden repaired. I said yes and he hasn't done this. Its been several days. I looked it up on the wiki and it says that his dialogue option to fix the garden will bug out, the task wont be complete, and the dialogue to have him repair the garden will disappear. Is there any way to get him to do it?

Reload a previous save and don't do it.

Who the hell is he?

Reload to a previous Save and try another dialog option.
If you leave the decision to him, he will also eventually make the repairs.

It can also take more than "a few days" sometimes, especially if you're just waiting around the Keep.

But yes, it's a know bug. You might be stuck without those repairs.

He's the majordomo of Castle Volkihar, the guy who claims to be above all the petty bickering of the other vampires.

After you finish the main Vampire-side story, you can ask him to fix the balcony, which gives you access from the Soul Cairn room to the main castle building. This is also better for your health when you FT to Castle Volkihar, since you can port to the Balcony's marker and walk in, instead of porting to the castle's marker where you're prone to eat Dawnguard Scout ambush teams.