This looks like they are using voice messaging to text you. Annoying, but quite common these days, and doesn’t necessarily mean anything nefarious.
If it were me, I would ask them more questions. Ages of children for child-proofing purposes, the city they are traveling from, etc. Just to get a better feel for them, their communication style, and their timeliness of responding, to increase the possibility of it being a good fit. This interchange, IMO, is actually more important than the actual answers to the questions.
Having said that, I agree there are some red flags here:
1) For when is the booking? If it’s soon, I would be cautious, as sometimes people get evicted and are trying to find another place quickly.
2) For how long is the requested booking? This looks to me to be open ended “until they find a house”. If it’s longer than 28 days, definitely fill out and have them sign a state-specific rental contract, and run credit and criminal checks, just as you would a long-term tenant.