I've successfully used FB Marketplace several times, in fact just rented a house for April from marketing the house there, had 96 inquires and 23 that took the time to submit the pre-screening application.
I used a questionnaire that I made on Google Forms that I read about on here and I love it, it's been a real time saver. When someone messages on Facebook, I send a copy/paste of the same response to everyone that the house is still available and if they are interested in viewing the home to complete the pre-screening application (with the link attached)
Another think this does for me is I am able to match up the Facebook profiles with the applications received and yes of course I look at what they post and what there photos show as the kind of person they are, if they have pets they didn't mention, are always drinking in photos or drug use, etc
I did a quick search and found the original thread and have attached it to this response, I certainly can't take credit for this awesome idea.
https://www.biggerpockets.com/forums/52/topics/448203-pre-screening-questionnaire
Mark
Edited to add: Ok so that's not the original post I saw about Google Forms, I thought it was but you get the idea