I think it depends on where you are and what state you are in.  When I was selling in Oregon, for a USDA deal, if it wasn't in the contract, it wasn't an issue: ie - if pest work wasn't asked for in the contract, the USDA lender didn't care.  However what USDA did care about was property eligibility - essentially (in my cases) it couldn't be a property that had income generating potential and it could not have "outbuildings" on the property - no barns, no storage sheds, etc.  Couldnt be a farm or in an area zoned for agriculture or farming because there was potential income generating possibilities.  

I have never worked with these.

I wouldnt know this.

I've never ever had a lender given the home inspection. However ever issue noted by the appraiser must be addressed and have a re-inspection by the appraiser.

I haven't had it come up in my area either so it may be more of an underwriter issue.

These days escrow or attorney will send the funder everything - termite, well, and any inspections, thus opening up all work to be completed. Assume if there was an inspection the conditions of the inspection become a part of the deal. No inspection, and not mentioned in the appraisal, and no credits or mention in the contract the item may not become a part of final conditions

If it is this is new to me.