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?

Maximum you can keep for an hour from the time you heat up the milk. Any leftover will have to be thrown away. Another way to know is by the smell. Weather also plays a very big role. If you put it openly in a hot and humid day, you may not even be able to wait till 1 hr. By then, high chance the milk will be spoilt already.