Is my cash-out refi a no-brainer? Or am I missing something?

[Bryan Cerro]

This is my first/only property so I am very much a learner still, advise on everything welcomed. 

I've been house-hacking my duplex (other unit rents @ $1,000/mo) for a few years and believe that I should cash-out refi so I can purchase another property but I have a couple of questions. 

Here are my stats:

Purchase Info: $139,900, 30yr @ 3.125% and I put 5% down (looking to get rid of my PMI through the refi)

Current Loan amount: $126,365

Conservative guessessment value (2020): $200,000 

Refi loan amount (75% LTV): $150,000, 30yr @ 3.374%

The data provided by my friend/loan officer shows over the 30yrs I could save $48,059 in interest/PMI, my monthly payments would go from $1370 to $1135 and I would get $14,921 in cash after fees.

Could someone explain the numbers showing how the 20% would be paid to eliminate the PMI? My lender said the PMI is just gone - I guess I don't understand why the bank would waive free money, they were charging me before, if they didn't have to.

Does it work like:

$139,900 - $200,000 = $60,100 (difference in home value)

20% of $200,000 = $40,000 (buh bye PMI?)

$60,100 - $40,000 = $20,100 Cash return - $7639(fees + taxes) = $12,461 cash in hand (close to the estimate of $14,921)

I have been slowly working on improvements myself to learn the value of the work before I look at outsourcing, but that means it is a slow going. What improvements would you consider worth prioritizing before I cash-out refi? Or should I just go ahead as it? Furnace/Roof/Water heater are maxing on life expediencies (~15-20yr old) but I was going to ride them till they died. Exterior windows/doors are looking rough and were my priority to scrap/paint. As well as replacing fixtures/outlets/lighting inside.

Are the fees appropriate? $635 appraisal, $70.50 credit report, $455 processing, $60 recording, $795 underwriting, $840 hard insurance reserves, $4020 taxes reserves. I will get paid out from my current escrow and use that to reduce my fees, ya?

Let me know if I left any useful data out, Thanks! Bryan