You can mix FG and CG representations by using them both with a mixing parameter lambda (between 0 and 1) That specifies the weight of the FG contribution.Then you can make lambda dependent in the position in space and thus focus on an interesting part of the system. These methode are still under development. It is not a good idea to mix FG molecules with CG molecules in the same space.

A force field is a self-consistent representation of physical properties. In general, you can't mix and match things like this. I have, however, seen some instances in the literature where specific parameter sets are applied to do such mixing. See if you can obtain and apply those parameters if you want to go this route. In general, though, I tend to think that atomistic should be atomistic and CG should be CG.  If the protein conformation is sensitive to lipid conformations (and many are), then you're going to be missing those effects by using CG lipids.

Yes, you can! But it would be better to be homo-phasic on the modeling. Try using one set of technique either.

You can mix FG and CG representations by using them both with a mixing parameter lambda (between 0 and 1) That specifies the weight of the FG contribution.Then you can make lambda dependent in the position in space and thus focus on an interesting part of the system. These methode are still under development. It is not a good idea to mix FG molecules with CG molecules in the same space.

There are ways to do what's called adaptive resolution coarse-graining, which sounds like what you're talking about.  I've never done it myself, but I believe the principle is sound.  You may want to try looking at the link I've attached and similar papers.

http://pubs.acs.org/doi/abs/10.1021/ct401029k

The people behind the Martini force field have actually done this a few times for soluble and membrane proteins and, more recently, for DNA.  Browse their website (http://cgmartini.nl) and read the relevant publications, they also have a tutorial for a combination of OPLS (AA) with Martini (CG), although it is rather complicated to prepare such systems with their approach, since it requires generating new, hybrid AA/CG parameters dedicated to the system you study.

Another example is the PACE force field by the Schulten group, which I have personally used occasionally.  PACE uses a united-atom model to represent proteins and the Martini topology for lipids and the solvent.  Its upside is that it requires very little parametrization on behalf of the user and, to make things easier, there's an automated system builder for PACE in the CHARMM-GUI website (http://charmm-gui.org/?doc=input/cgbilayer).  Its downside is the fact that you need a specially modified version of NAMD 2.9 to use it (although it is rather easy to compile it) and everything that comes along with that requirement: you can't use polarizable water (so, you can forget about using long range electrostatics), only phospholipids are currently supported (since  NAMD has no LINCS-like constraints algorithm, any ring structures are poorly represented, so no cholesterol) and the Langevin thermostat/barostat combination tends to implode when Martini is involved (this is a problem vanilla Martini also has on NAMD).

If we are to trust the PMF curves and solvation energies provided by the authors of these mixed approaches, then the CG/AA combination seems to work.  However, it all comes down to what properties you want to measure for your system of interest.

If you are interested in protein-lipid interactions, hydrophobic mismatch etc, I would recommend using either a purely AA model or a purely CG one (surprisingly, despite the loss of detail, Martini can model hydrophobic mismatch and the energetics of protein-lipid interactions with significant accuracy).  If, however, all you want to do is see how a protein behaves in a membrane for a specific time, you can use the hybrid approach.