The phrase " i'm lovin' it " (note how I wrote it) is a McDonald's slogan. We could give you a long explanation on how it works grammatically and how native speakers understand it, but the fact is we don't use it in daily speech. If you say this, it sounds like you're quoting a McDonald's advert.

A: Are you enjoying your dance course? B: Yes, I'm loving it. That sounds ok to me.

No, not really. That's just a slogan for McDonald's. Sometimes we might say something similar though. For example, if someone starts to get famous they might say "I'm loving all this attention". However, it's much more common for people to just say "I love .....".

I do not understand the reference to hamburger, but people do use the expression "I'm loving it" to express a feeling of enjoyment.