She and he have a relationship that predates you and it does sounds likely that there are some unrequited feelings in play that are likely to create complicated situations in future. However he's allowed to have that relationship and I for one would not question it. I'd observe it, decide if I'm ok with it, and then move on or not.
Having said that my dp is friends with almost all his exes and they are lovely girls who I like, without exception. We spend time with them, he spends times with them without me there, I spend time with them without him there, it's fine.
Twice a week is a big investment of time though... That is actually the part that makes a little bell ring in the back of my head tbh. Once a week would be a more normal friend cadence unless they were doing a shared activity like a sport that has say a practice plus a match every week, something like that. Twice a week staying in just the two of them, every week not just during a time when one of them needs a lot of support (e.g. during a bereavement) is a very high degree of intimacy. Tbh I'd expect that they still have sex / cuddle etc. Which again, is their business and their relationship predates yours, so it's a fit in or fuck off situation really. I'd not trust words in this situation. I'd read the actions and assume the truth (without being arsey about it iyswim - people are who they are, and they sometimes lie even to themselves).
The date thing is fairly weird if she is calling it a date. If she's just wanting to hang out and get to know you, that's not weird. Again, I have friendly relationships with several women who predate me in my dps life. It's fine, they're nice lasses.
You've got to decide what you're comfy with tho op.