RE: Is My Gridcoin Wallet Working Correctly?
They should be getting modified, problem here is whether it's windows being fussy about updating the modified date or you wallet being strange,
A screenshot of your wallet would be better in determining if it's working correctly, If it is in sync and you see transactions coming in from GRCpool then it is working correctly.
Additionally if your wallet is unlocked the little uparrow thing should be green to indicate you are staking if you are bothered about staking your coins.
As posting in other comments, backing up wallet.dat and gridcoinresearch.conf will keep you coins safe from anything weird going on, also if you can manually close gridcoin before doing any system restart or shutdown to be extra safe but in general you should not need to.
One last thing I'd like to add, You should make sure gridcoin has a rule allowing traffic through your firewall or antivirus firewall, This will allow incoming connections which will in turn help your wallet stay in sync.