Kalene's scenes should all set you to 0 lust (although some will leave you with a moderate amount of fatigue, it varies), which should mostly get you set through the first bit of the game that's currently in. Unless you push her away, which will leave you at very high (80+) lust and is intended to be a little bit of a rough start for a sexless run. So far I've mostly been focusing on adding more sex-scenes rather than encounters to get rid of lust without sex, but I did add the outfits to give players ways to manage lust. One prevents passive lust from walking from room to room, one prevents you from ever going over 70 lust, and the other removes fatigue added by sex, so you can indulge to get rid of lust without having to worry about fatigue building up from it. I do intend to add more ways to manipulate stats outside of sex encounters in the future. Could probably do to throw a few small ones into the next update.
As for the story, the intention of the trial so far isn't to avoid having sex completely, it's to escape. You can (and should) have sex as you like on the way, just be careful about indulging too much or falling for a trap. Once the game's a bit more developed and you have sufficient ways to manage stats, having 100 lust, fatigue, and lewdness at the same time will drop the game into a generic bad end.
I will also say, the sexless path is not one of the "canon" paths, and I'm mostly including it so that whenever I make a scene I always have a way to avoid any content and still have a full playthrough. I've toyed with the idea of having a sexless run unlock a reward or something, like revealing hidden stats on the stats page or giving detailed stat change messages on subsequent playthroughs, but that's quite a ways down the road.
Finally, you're not really intended to have deep insight into what Alexis thinks of things, I've had to add some here and there just to have a coherent story and inform the player, but otherwise, I've tried to keep him a blank slate and the player will decide that through their actions and their own interpretation of things. Some of the questions you've asked will be answered in future encounters though.
Edit: One thing I might add because there's no way to really convey it in the game, male Alexis isn't necessarily actually a virgin, other characters might speculate or have an opinion on the matter, but whether or not he actually is, is an example of one of those things I leave up to player interpretation. Female Alexis is physically a virgin though, having just gotten her body and all.
