Plus if you ask a bit higher and get it you always have you inspections and contingencies to get or ask for a reduction in price if you find things that hurt your numbers.

My agent wants to waive inspection contingency.

Remember that your offer to purchase is always going to have an exit contingency for financing should you need it. 

I always sign the contract "contingent on financing" so I have an out.

Waive contingencies. 

There would need to be two separate contracts (it's probably okay if each contract is contingent on the other in a "conjoined closing"). 

With remote rentals, you just need better contingency plans. 

Is it a good idea or an unreasonable ask in my offer to have a contingency stating I'd like to get a professional appraisal done and offer is contingent on my satisfaction with the findings? 

I mark 1 both, not cash, and put in remarks "contingent appraisal and approval of finds per hard money lender" to avoid risk of earnest...I have due diligence period for 10 days anyway and my lender is way less that that, so i would not risk my earnest money for the most part...and I want to put in "cash" offer....wondering if I could do both boxes, or if matters..what do you do?

Make the offer contingent on the unit with the slow/late/tax return paying tenant being vacant at closing.