our title insurance provider is declining to offer coverage stating that since we took it out of our name and even though i quit claimed in back, that voided the coverage. 

Needless to say, I passed.After I notified the listing agent I declined the counter offer (he has been very helpful), he sent me an email Monday evening saying suddenly they are receiving offers on the property and she will take the highest offer she receives before 5pm Tuesday.  

apartments.com sends me the report and I accept/decline from there.as far as your second question, I recommend reading the section of the MN landlord Tenant laws regarding tenant screening (entering into the agreement)https://www.ag.state.mn.us/con...A landlord must return the applicant screening fee if:The applicant is rejected for any reason not listed in the required disclosed criteria; orA prior applicant is offered the unit and agrees to enter into a rental agreement.If the landlord does not perform a personal reference check or does not obtain a consumer credit report or tenant screening report, the landlord must return any amount of the applicant screening fee that is not used for these purposes. (11)

They are notorious for collecting an up-front "due dilegence" fee and then finding a reason to decline it. 

That sounds excessive.If it is not in the contract and you don't want whatever service they are offering, I would probably decline it.Probably good idea though to rekey after closing as you don't know really who has keys or how many copies there are.   

The property is rented out but I'm concerned that as the neighborhood declines it will be harder to rent at market rate and/or the quality of renter will decline.

Don't make the mistake of declining that offer.

If the population is static or declining, the existing housing supply meets demand, so prices do not rise significantly.Rents follow prices.Higher prices reduce the number of people who can purchase, increasing demand for rental properties and increasing rents.Lower prices enable more people to purchase, decreasing demand for rental properties and decreasing rents.If you buy property in a low-cost city, your rental income will not keep pace with inflation.

Everyone has lots of opinions but few actually look at more data or think through the reasons for the decline.

In terms of the due-on-sale clause, in the past 40 years we've generally seen a declining interest rate environment.