They offer warranty on every appliance.

At this stage, if there are a couple comps you think are valid, but the appraiser didn't use, I would contact the bank to contest the appraisal. 

You could do all of these yourself, but the issue probably has to do with validating the numbers.

CaN anyone suggest a home warranty company they are happy with the service and turn around responses to service rush orders?

No subject to needs to have title transferred to be valid.

The lots are smaller also (.16-.21 acres), but it's a new home with a warranty.

Is it a warranty deed, or a quit claim deed?

If that is your goal it is a valid strategy. 

The exception is that hard money lenders may not care as much about your FICO score as they do about the validity of the deal you have identified or the opportunity to generate a return on their money.

You will sign an affidavit attesting to this, so failure to do so could be considered mortgage fraud.If you have a valid reason for needing to move (unexpected job transfer, death in the family, etc), it's generally assumed moving would be allowed without repercussions.