Newer gas fired water heaters (mine is 10yr old) with closed chamber have special chimneys where your exhaust and intake go through double walled pipe with counterflow, which helps with energy recovery (exhaust goes through inside pipe, fresh air goes in outside pipe and gets heated by exhaust gases). That also means you don't need to have proper intake where the heater is (but there still needs to be some ventilation).

Yep, it is subject to building code requirements. This is why installing ducted vent hoods usually requires a permit etc...