I furnished some with craigslisted twin beds and dressers (roughly $300), so my walls wouldn't get banged up on move in/out.

Would you trust what was behind the wall after the drywall was replaced? 

I have 1 week to get the proof of funds so that we can close on this deal, and I feel as though I'm hitting a wall.

Does the seller want cash now, or would they be interested in seller financing so that they can retain some cashflow after the sale and not have to worry about a tenant not paying rent?  

Make sure you retain these documents and you should be fine.

I have a rental property in Costa Mesa, CA and a tenant claimed that after she cleaned, her carpeted floors in her room were wet and she was worried about mold being under the carpet and in the walls.

But the carpet and walls are super dirty now.

Anastasia,I had the same thing due to a tenant overfilling the trash can, leaving the top open next to a concrete wall and an empty field = Free lunch for all! 

Is there a way to hire a company to manage and maintain the buildings while I retain ownership and part of the profits?

We didn't do much to the exterior so it would blend in and not attract the wrong attention, but the interior has inexpensive but modern finishes, brown-grey laminate throughout, light grey walls and white trim, cool pendant lighting, open floor plan, you know the template :)