Hi sani_rae, hope you’re enjoying your new violin!! The liquid rosin is not for the bow. You can use a drop in case that the pegs are slipping.
You’re instrument not staying in tune for a long time is because the strings are new. It depends of the material of the strings how long it takes before and if they stay longer in tune. If the temperature and humidity doesn’t change much that helps too of course. Where I live temperature changes a lot during the day. And I’ve noticed that if I keep my violin in its case when I don’t play it, it stays in tune longer. If I leave it out of its case it goes out of tune fast because of the temperature changes.
Hopes this helps you a bit 🙂