What an impressive piece. I wish I had such acquaintances
I would not do a "deep"cleaning. I sort of like the patina on the helmet bowl.
The helmet plate looks like it has some (white) residue of brass polish.
I would start to remove that with a toothbrush and some soft soap.
The side posts and kokarde have some oxidation that I would also start to try and remove with a toothbrush and some soap.
The liner is probably original. Officers helmets have these types of liners.
Best regards,
Willem