Short Answer: everyone has their own style when it comes to applications, and you should take some time to decide how picky you're going to be about it.
A lot of what you're going to want to ask, and how much you want to ask, is going to depend a lot on what kind, and length, of game you're looking to run.
Is this a short oneshot where you'll never have to run these players again if you don't want to? Oneshots and shorter adventures can get by with a bit less interrogation than intended long-running campaigns, in my experience. Are you setting up for an epic campaign possibly spanning months? That means you'll probably want to be pickier about your players, since switching out characters and players in medias res can be a disruption.
Everyone has their own red flags for people and types of people they won't feel comfortable gaming with, and as you go through this process, you'll likely gather up a bunch of your own.
Basic questions/prompts that are a good idea for any length:
- What's your knowledge/experience with Pathfinder? (Are you, as DM, willing to take the extra time to help newbies figure out the system?)
- What's your knowledge/experience with roll20? (Are you, as DM, willing to take time to help newbies figure out the website?)
- Tell me a little bit about yourself
- Give me a rough character idea so I can get a feel for your style/Tell me about your favorite character that you've played in the past*
- We're going to be using voice/video and voice/etc. to play. Do you have the ability to do that?
*This can be a spot for potential flags, including murderhoboism, though personal interpretation will vary by DM.
If you're looking to gather up a group geared towards regular, long-running play, it may be worth it to have a 2-step process, where you chat 1-on-1 with possible players to get some more in-depth answers. Here are some of the questions my group used when interviewing new players to add to our ongoing long-runner:
- We play regularly at [time] on [day of the week/frequency]. Can you commit to making at least most of the sessions?
- What sort of themes and concepts do you like to see in D&D campaigns? War conflict, political games, intrigue and skullduggery, etc.?
- What do you like out of D&D? What are some past stories you've played through that you've liked?
- Do you have any "hard NOs" or things you don't want to see at the table? Either player-wise or plot-wise.
- Do you have any questions for me?
Red flags can end up very personal to the DM in question, and asking for examples of those might be better suited to a discussion forum. (E.g., a red flag for me is anyone pitching a concept specifically requiring a 3rd party homebrew outside of a very narrow list. Other DMs/groups might not have a problem with that.)
