Needs only carpet and paint.My first question is this: Even if I had a buyer lined up at $90k, is 2 weeks long enough for us to close on this property before auction?

Think about that the next time you are at Home Depot and wonder if you should go with the cheaper carpet and save 30 cents. 

I have even had customers come in where I work and overflow the toilets there causing $100's in damages with replacing carpets and what not because the didn't know how to plunge or just panicked.With an older 2.5-3.0 Gal model you can pretty much be assured that if it clogs and your tenant decides to flush it again as a way to clear it, you will have an overflow and have a mess to deal with.  

After a long and messy eviction, I was hoping to get back on track but rents are coming in later and later each month and I have questioned a large expense several times, which I did not approve.

There are a lot of basic items (tax prorate, home owners fees, possession terms, etc) that can get messy, esp. with a BAD / boiler-plate reassignment contract.  

Also, in a SFH, what are the pros and cons of removing an ugly carpet?

This is the defining competitive element of my business.With this machine, carpet, tile and grout cleaning jobs are faster, cheaper and possibly better than the most skilled cleaner using some previous generation equipment. 

We are already over $5000 in repairs to plumber & drywall contractors (and $200 to an electrician to flip a breaker on a Saturday because she was afraid the whole house would burn down due to the water-logged foyer light...and so turned off the Master breaker instead of just isolating the light) and now she's saying she doesn't want carpet reinstalled in the basement because it might get wet & moldy and "affect her boys & dogs".

Her is a before/after pic of one of my most recent rental acquisitions in which I removed all carpet and installed vpf.

With some damages you need to take into account normal wear and tear, or even depreciation, such as on a depreciable item like carpet.