2nd starter Nissan or aftermarket? Aftermarket unit's don't always match up well with the flywheel (gear teeth) and you get grinding. A local shop here that works on a fair number of Z's only sources them from Nissan to avoid this issue.
Rough Engine Issues: You'll need to run your ECU codes and see if any system errors are being reported - easy to do this yourself. Hopefully you haven't lost an injector - shaky and rough is how that feels but it could be some other things too.