If I have already warmed up the breastmilk, and baby does not complete drinking it, how long can i keep it in the open for? Can I refrigerate after?

Personally, I used to throw away any unfinished milk an hour after I warmed it up. This is because bacteria thrives in warm room conditions and especially in a humid climate like Singapore, the amount of bacteria in the milk would increase as the time passes. These bacteria can cause upset stomachs so I rather "waste milk" then have my baby suffer. Do not refrigerate leftover milk for your baby's safety. What I did was to freeze my breastmilk (after pumping) in small batches of 120ml instead of 200ml and above. This way I can control the amount that I warm up and would waste lesser this way.