>>227524323She's starved of affection more than anything else, but what she feels for Madoka is undeniably romantic love. It's more questionable in Madoka's case: normally I'd say no, but she's a depressed mess of a person despite having a near perfect life, and while she's an empath who clearly loves everyone, what she feels towards Homura is unmatched and a common factor in every single timeline.
In terms of sexual orientation, we have no bloody clue, and I don't see the series ever tackling that.