A deposit is standard for DD and maybe to pay for the appraisal.  

Yes, in my experience appraisers have to pull COMPS that are in the same city as the subject property.

We are not appraisers, and we cannot always be correct on ARV, but we only put our best estimate forward, and we do double check the quality of that estimate to make sure it was solidly accurate.

PIN has excellent Everything reports that bank appraisers do use to assess the value of a property but you're better off working with agents in those markets and getting free current market analysis reports.

And other than FLA ( starter homes) because appraisals came in low and they were fha buyers we would never retrade..

Not only are those deals tricky, but you also need an appraiser to agree with the values needed to make a deal work, which, lets be honest, can be a bit of a crap shoot. 

Increase in family size:A Borrower may be eligible for another house with an FHA-insured Mortgage if the Borrower provides satisfactory evidence that: • the Borrower has had an increase in legal dependents and the Property now fails to meet family needs; and • the Loan-to-Value (LTV) ratio on the current Principal Residence is equal to or less than 75% or is paid down to that amount, based on the outstanding Mortgage balance and a current residential appraisal.

Let them know they might get more money by listing with you and selling to a third party, however, the seller should consider the contingencies that enter into it, for example, inspections, appraisals, mortgage approval, etc.  

Getting a 6% instead of a 6.5% doesn't save you squat if you have to bid $30k over asking with an appraisal gap and then replace the roof 6 months after you buy the property because you had to waive the inspection. 

a low appraisal could easily wipe that out.Yup.