@jwenting flights to Cuba are legal (for a few years now), however cruise ships are not anymore (they were for a few year period before being outlawed again). Technically no more travel ban, however, you must get a waiver from the Treasury department certifying that you aren't going to fund the cuban regime, and choose a valid exemption for travel (such as 'Support of the Cuban People' for tourism)

I'm asking this on behalf of someone I know, who is pending asylum. If they were to identify to CBP, their re-entry to the US would be denied, and their case thrown out.

While true that the airline can't give you the check, they can "ask" for one. This is the practice that's coming to an end and has been phasing down since 2015. The best primary source from TSA is here: tsa.gov/blog/2015/03/26/… "As more and more travelers obtain KTNs, soon, travelers without a Known Traveler Number or KTN, including those who previously “opted-in” via a frequent flyer program, will notice a reduction in the frequency in which they are chosen for TSA Pre✓®."

Updated to mention where you can possibly find some roach spray.

By infestation, I'm just clarifying that there is such a thing as an unacceptable level of cockroaches, but since you're saying they all look clean, it probably won't be a concern. You can generally ignore negative reviews that are solely due to cockroaches, unless they mention seeing 10s of cockroaches, instead of just a couple, as that would be an infestation rather than just some visitors.