A level is friendship is fine. There's a difficult dividing line for the friendship may prevent the professor from being impartial.
From my own perspective, I'm interested in my students and want them to do well. I'm also keen to know how they're getting on with their studies and their preparation for employment. That automatically brings with it a level of friendliness.
In many cases, I also have a duty as a personal tutor. Part of that means keeping an interest in a student's welfare and helping to put support in place when necessary (it doesn't necessarily mean that I'm an expert in this support, but it does mean knowing who to refer students on to for it).
In many cases, it's much better to talk over a coffee.
A student might find me eating lunch in the canteen and that might be the best time for the time they feel comfortable talking to me. To me, that's generally fine too.
And I certainly know of professors who go above and beyond the call of duty to keep in contact with students when they're worried about them, for instance when there may be mental health issues involved. That can be the right thing to do in some situations.
Likewise, I've often gone out of my way to support students who want to push themselves academically or explore their options. I want students to do well, so if that means staying late to talk through ideas, sometimes best done with the aid of a beer, that's fine too. Likewise, I've encouraged students to join extra-curricular activities that might benefit them (such as tech communities), some of which I attend, so there can be some social crossover there too.
There are definitely former students who considered me as a mentor (and, I still stay in contact with many of them - some still consider me a mentor even years after they graduated).
I still remember when I started university, the very first meeting between a small group of us and a tutor involved him pouring a large glass of whiskey for everyone in the room (probably an expensive whiskey, but I wouldn't have known the difference). And, there were a lot of social events which, if you didn't take part in them, the tutors would have been worried about you. So, culturally, a certain level of friendship would be both expected and encouraged.
Now, that doesn't completely answer the original question regarding where the dividing line is.
For the example given, this does sound like a very close relationship. The danger would be if other students think that the friendship has crossed the line, or that they feel that they are missing out on a similar level of contact.
If the professor is happy and able to teach and assess you impartially, that's fine. But if the way her time is being monopolised (for instance taking up her office hours every day) means that she's not able to concentrate on her other duties, you might want to cut back, if only to be fair to her.