I recently moved into a small apartment with an exposed water heater which uses natural gas. I found the major constituent in natural gas is methane, but was unable to determine if ethanol is also in natural gas. Worried about incidental exposure through alcohol fumes from the pilot

NOTHING to worry about at all.

Ethane, not ethanol. Natural gas is 95+% Methane, balance other alkanes. The gases burn and even if there was ethanol, which by the way is a liquid, it would become CO2 and water vapor.

The problem is leaks, and explosion from contact with a spark or flame.
A scent is added to the gas so that you can detect a gas leak. Do not touch a single light switch or anything at all electrical and call your supplier.
'Exposed' I assume means in a living area? That may not be code where you live.
If you wish to get out of your tenancy, you could check with the building inspector and possibly use it as leverage to get out. Don't count on your landlord paying to move it and keep you as a tenant - it will be expensive.

If you are worried about ETG there must be alcohol abuse issues... you won't be using this for an excuse. It can't possibly effect that.