Often times the sale of these properties is directly derived from the rents minus the expenses.  

I firmly believe that wealth is borne of equity -- derived from both forced and natural appreciation -- and that cashflow is your buffer to protect your equity.

If the property is new or maybe less than five years old, an appraiser may use the "Cost Approach", whereby and land and building values are estimated to derive the value. 

They determine your dti derived from your reentals by taking 75% of your rental income, subtract depreciation and your expenses shown on your SchE.

The ones that I am holding are relatively cheap but they are giving me really good cash flow (Combined value for these 2 properties is less than 200k but rent I derive from these 2 in total is around 2.5K).

Now, if you are trying support a valuation to some 3rd party then the BPO is going to be more credible to them than your own assessment, that you derived from publicly available sources. 

US News and other local publications will have that information and how they derive to that ranking class. 

4) My experience with banks has been difficult since my income has been mainly derived from income properties and freelance work, so I'm curious how easy are banks to work with to get approved for a new loan with a 1031 exchange?

Life is a magnificent journey and much of the joy you can derive from it involves performing meaningful work. 

Value isn't traditionally derived unless it is ready to build lots inside a developed city.