Airi's face has got decent facial expressions however there are not too many of them. But it's true what you say about the teeth. It's not very noticeable on Airi but all the other girls have that wierd shock + disgust kind of smile.
It's visible on Airi but mostly on animations (which are of really low resolution). If you check out the banners for update posts on Ci-En, you'll notice how, for example, Kappa is making Airi make a literal derp face from hell. Maybe later on, Kairi will add in high resolution shots, like in the first game, which show up when you trigger certain animation for the first time. That's when we all will be scarred for life...
Is there any type of prostitution in this game if yes how can achieve to do that?...
What do you mean by prostitution? Giving or taking?
You can "use" prostitute services every now and then when you go to sleep in the tavern. You will have knocking event in the middle of the night, with black-skinned whore asking you if you are interested in her services. She will eat out Airi for 10 coins.
Other than that, you have some options to be a whore. You must first equip a whore/prostitute card in the inventory (I think you get it from the merchant lady in the forest or can learn it from someone - it changes every other update so you need to look it up yourself how it works right now).
With that done, you will have few options to whore yourself out. Merchant guy in the forest (you can blow him), barbarian guy (missionary), one guy in the castle (smelling/licking feet), big knight guy (unique cow girl scene but required some high love stats to trigger).
If you lose to debt collector and have above 300 coins of debt, you get sold to brothel (though nothing interesting there). Same happens if you refuse two times to the slaver boss after losing.