does anyone else experience potential tenants that don't want to fill out an application?

There is little downside as the no eviction rules only applies to applicants: https://www.houstonrentassistance.org/landlords

Do I use the same criteria as above and invite the first ones who applied & fit the bill to do the background and application check?

A lot of folks want to compare investing in real estate inside a plan to with non-plan funds and that is a non-applicable way of thinking. 

Some other features landlords commonly look for:Automating late fees (the level of complexity you require can impact the software that's a good fit)Logins for multiple employeesDedicated mobile app for your tenantsFull accounting features OR alternatively, integration with your preferred accounting platformDigital document signingTenant applications and screeningAgain, depending on which of those matter to you, one software will be a better fit than another.

You do not own the mobile home, just the lot and things like septic tanks  / water wells if applicable. 

I am having one or two applicants everyday and some of them really want it and are willing to pay several months upfront.

Last week, purchase mortgage applications increased 6% nationally, up for the third week in a row.

You can start the application now but the SBA has a temporary stay on all loans that aren’t the PPP till the end of June so you need to make sure your Seller is very patient... and SBA loans aren considered fast in normal times.

It has the most applicable information.