The answer to your first question is that it probably doesn't make sense to apply fix press/berendsen or fix temp/berendsen to groups of atoms that are in rigid bodies (i.e. where fix rigid has been applied). Even though these are not time-integration fixes, these berendsen fixes are designed to be applied on a per atom basis, so it doesn't make sense to apply them to atoms that are part of rigid bodies.
The answer to your second question is yes, it should be fine to apply fix rigid to a big (1000 - 10000 atom) nanoparticle embedded in a fluid that does not have fix rigid applied to it. Although I've not done a simulation like this, I imagine it should be possible to do it as you suggest. Should be no problem with loss of interaction between the particle and matrix, as long as you leave those interactions on, and they are defined correctly. You'll probably want to apply only fix rigid to the nanoparticle, and not apply fix rigid to the matrix fluid but instead apply a regular time integration fix to the matrix fluid.
Paul