The lawyers will normally decide to offer only no PPP options as not to possibly conflict with the law, so the lender is mitigating possible risks in not being compliant. 

We manage several hundred tenants and know how to handle this and we know the laws in our state.Giving cash for keys definitely does not feel good but a protracted eviction in our tenant friendly state of 3 to 4 months, which is the normal plus attorney fees will easily exceed $10,000 depending on the monthly rental cost.

Is this normal?

They normally don't last long.

Normally 2/1 entire apartments in area go $1600-2100 ranges so these were surprisingly high for just bedrooms.

Normally, split between buyer and seller

However if it is a smart deadbolt and a normal lock on the door handle they will need that key bc they will inevitably lock that one on accident and lock themselves out. 

Normally I would remove this post as self promotion- the original poster is a lender.

If the tiny home is more like a medium home (600+ sqft) on a foundation, then you should be able to look at it as a "stick built" or normal home, just small.

Normally at minimum an appraisal is required to verify the remaining collateral is sufficient.