No, the full game will be commercial, as it has quite a lot of content and full voice acting. The planned price point is $20 USD, but if that changes we'll be sure to announce it.
It can't be helped. The cost to actually make a game with 10 distinct routes and full voice acting is not small.
The demo is available for free so I'd recommend you try it out yourself, but you do start off already in a romantic relationship, even if things aren't going the best.