quickstudy

In my (admittedly limited) experience, if a supervisor asks the same question repeatedly, it simply means that you haven't given the "right" answer the first time around and they are waiting for you to spot your own mistake. Quite a passive-aggressive tactic, I know, but unfortunately quite common.
You are in this program because you wanted to get a PhD, right? I think that switching to law school is a step too far; it might be just a temporary hiccup. Switching PIs is not as uncommon as people think, but at the same time it means that a lot of work has been wasted. It's also not a great thing to have on your CV; lots of future employers in academia might look askance at that sort of thing.
It's not going to be a popular opinion on here, but I would say that you should stick to the lab, beg him to let you finish the PhD, and in the meantime generate data at a furious rate. If he's adamant, maybe you could talk to other members of your advisory committee (if you have a good relationship with them and they can be relied upon not to tell tales). Perhaps a chat with a friendly postdoc might help too.

I think we can agree on the following: 
- Staying with someone who doesn't want to have you as advisor for an entire PhD is ill-advised.
- However, it is best to part on good terms. It remains to be seen what that means in this case. It may mean sticking through the MS or it may not. But that consideration should be taken into account either way. Other important considerations are the OP's well-being and his/her next steps, once there is a decision about what those are. 
- If New Prof is an option, of course the OP has to talk to him directly and it's not enough to rely on rumors you hear from first-year students. However, I don't think that talking about being "rejected" by another professor is useful here. It's more appropriate to think of this as a classic case of incompatibility between advisor and advisee. That doesn't imply that the OP can't do good work, or at least that's not what the OP writes in his/her post. Again, I would approach NP in good faith and let him decide if he thinks there is potential for an advising relationship there or not. Don't overthink it and don't anticipate his considerations without letting him run his own calculations. You have to be your own champion; if you don't have your best interests at heart, who will?
- Going to law school would be a drastic and unnecessary step at this point.

At this point, your PI isn't going to change. If you decide to stick with him you'll be in for much the same communication style and interactions. Perhaps they're uncomfortable saying hard truths ("you aren't working hard enough/you don't know enough"), or perhaps they only have this vague sense that something isn't right and it isn't based on anything concrete. Is he used to dealing with non-traditional students? That might unfortunately be part of his problem (his problem, not yours!).
My translation of what your PI wants is for you to be more proactive. Not just saying "X doesn't work" and stopping there, but giving your own suggestions about what to do next in your meetings. Not just asking for advice, but offering 1-2 suggestions of your own and seeing which one he likes the most. He doesn't want you to mindlessly churn out data, but to work smart and explore the literature in depth.
These excessively non-confrontational, indirect people are fairly common in academia. I can't give you much advice about whether you should stick it out or change labs other than what I've said above (he's not going to change). It's unlikely that you can get the perfect combination of great PI + exciting project + ideal management/communication style, so you need to think carefully about what's really the most important thing for you.

I applied to EMBL program as well. Have not heard anything yet! Fingers crossed for both of us.