and if they do the underwriting now, then I get my offer accepted, am I locked in with this one particular lender or can I still shop around?

As for access, i put on a lock box and chang the code after they are done.

Setup a successful house hack, thus freeing up the $1000+ currently locked into rent monthly     2.

It also looks like an old t-lock shingle from the pictures, which means it’s old because they don’t do that type anymore, and you are not roofing over that if it has issues and it’s going to be a complete tear off. 

I sign a couple of documents ( Appraisal report, Proof of delivery, hazard insurance, loan estimate, Lock agreement) but my current loan Status is Conditional Underwriting Approval.

Would a good bargaining tool to lock them in for another 12 months and increase their rent at the same time by purchasing a ($300-$400) fridge.

There are numerous gadgets to purchase to hide your key under the vehicle in case you accidentally lock your key inside.- Know how to use a tire jack

There is almost 0 crime in the town, many people don't even lock their doors.I own a multi-family rental in Buffalo NY in what I would also consider a "B" area, regardless of age.   

I mean I have a lock box for that purpose but every time they lose a key and I have to change the lock box code than I than that takes me time. 

@Jeff Owen as everyone has said cap rates can be difficult to lock down especially in smaller markets.