This first property is a test case to see if I want to continue investing in CR (or perhaps mexico and belize later).

One lease is the owners brother which becomes important later on.

If you're looking for a more permanent home later, consider areas that are not just tourist-oriented but have good schools and community resources, which can be more appealing for long-term living.

Is it possible to take out a mortgage under our personal names and then convert it to the LLC later?

This raised some doubt and we communicated to our agent that we are not satisfied but she kept insisting “there’s nothing you can do” and “you went non contingent” Then later she sent an email saying we passed the 17 day inspection period which we didn’t know about.

I will call you later today. 

But inside your scenario is a workable 1031 that could later be converted into your primary residence. 

Had a pretty good experience in their "Challenge" ($7K) program that deals only with single-family investing.However, later that year, we upgraded (in theory, and in dues) to their "Preferred" (or "PIG") membership, so that we could invest (passively) in multifamily deals. 

8-months later, have you managed to make any progress?

This approach helps ensure that buyers have a clear understanding of what they are purchasing, reducing the likelihood of surprises and issues later in the process.Of course, this is market location and cycle dependant.