There's only about 2 types of work permit I know: closed  vs opened work permit: where the former has a condition of which employer the holder of the permit can work for (it's specified on the document); while the latter does not have that condition; hence, the holder of the open work permit can lawfully work for any employer.

That would be a allowed but they should be doing more due diligence and requiring a lot more documentation than what an asset based lender would require.

You can often get better rates with a national lender, but the customer service is non-existent, communication probably sucks, they may ask for the same documents multiple times, etc.

In neighborhoods that won't attract high credit score tenants, I've found that a stable job history with a MINIMUM of 1 year at current or previous job to be the best indicator of a great tenant. 

Is it a reputable company and will the documentation provided from the study hold up in an audit?

It depends on how the transaction is structured, and the history of the title and timing. 

A great REALTOR will help you gather rental history and the cost to own and show you good sites for pulling rental projections, but you will need to do your own calculations.Everyone's mileage varies.

I never give the system or the prepped documents. 

I'm an independent agent here in AR and I write a lot of rental property, with ~6 preferred markets and if the properties have some issues, age, claim history etc.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?