Crabs

Have you installed the dev version of TestFlight? The master version will cause issues like this as it isn't compatible with 1.3. When the crashes occurred for me they were at similar points as you describe.

Try rotating the blackheart fairing sides upside down, that allowed me to attach them.

There were two recent reports from the RealPlume thread describing this problem, you could try removing that first and see if it fixes the problem. As a workaround Part Commander can give you access to all your parts right-menu without having to click on the part itself.