My T does both psychodynamic and CBT. He seems to be reading books on pretty much all modalities though, he knows lots about for example DBT and can work with those things if needed. So maybe if you interview somebody ask them what they know about modalities other than those that they list as their primary ones? I like to have a mixture of different approaches since the T can adapt to what I need in a certain moment.

Having BPD myself, I'd personally bring it up since it affects me a lot. You said the primary focus would be dealing with losing your T, so you will probably have to bring up your attachment. Of course you can also say you don't want to attach to the new T, even though one might argue that you can't just decide that.

Regarding outside contact: plenty of Ts offer that without being trained in DBT specifically. Pure DBT outside contact is somewhat weird as far as I remember. I think I read somewhere that it's for example if you self harm, then it's okay to reach out at any time before you do it, but not after you've done it. So maybe it might be a good idea to ask things like when is it okay to reach out, how often, how fast can you get a reaction, and so on.

Regarding hugs: if you think that'd be something you'd absolutely need in case you get attached, I'd ask. It doesn't hurt if you ask but then don't need it. But if you're suddenly attached to someone who doesn't allow it and it's important to you, that might be a problem. But maybe it would also be good to learn that you can be attached and feel safe without hugs?

I don't think you can decide whether or not you'll get attached to somebody. To me it doesn't sound too bad to be attached to two people though. It might distribute the intense feelings more onto two people instead of one? I don't know whether it would be like that of course, but I certainly don't think it would only be a bad thing to be attached.

Regarding gender, I think go with whatever you feel more comfortable with. My previous experience was always that I fell in love with men who listened to me, but I do not feel attracted one bit to my T. There's also some transference with him that I'm pretty sure comes from my mom, so I think that could happen with both genders too. Maybe don't focus on the gender too much at first and try to find somebody who matches your other needs?

In case a T doesn't specialize in DBT, I think it'd be good to ask whether they've worked with BPD before. I'd also mention what you're there for, what you're looking for and then ask what their general approach would be.