Car is it possible for something to put out an odor in a car something mechanical

It sounds like there may be an issue with the gear shifter mechanism in your 2000 Ford Focus. The loose shifter and bad odor could indicate that something has broken or worn out inside the mechanism, and it might not be fully disengaging the gears. The fact that it still shifts into reverse suggests that the problem is not with the transmission itself but with the gear shifter assembly.
To fix the issue, the gear shifter mechanism will likely need to be disassembled and inspected for wear or damage. Any broken or worn parts will need to be replaced. It could be caused by the bushings or the gear shift cable that connects the gear shift lever to the transmission. These parts could be dried out, loose or broke. It is also possible that the linkage inside the gear shifter assembly is corroded, or there's internal issue with the shifter mechanism.
Given that it is a manual transmission , it is important that the vehicle is properly repaired as soon as possible to avoid further damage to the transmission or other components. It is best to take it to a professional mechanic to have it inspected and repaired.

Possibly something preventing shifting at shift mechanism. First check if any obstruction of shift mechanism. Have someone shift while you visually check movement of shift mechanism. Ensure mechanism travels fully with no known obstruction.

This is not possible, Benzene is a component in gasoline but it cannot be isolated. The odor that you smell is something else.

Very possible. The code for the fuel cap is probably one of the codes for a pressure leak in the gas tank vent system.
If it was not smelling before the brake repair, I would take it back to the shop that did the work.

Well the smell is probably alcohol but that does not tell you much.
Most any auto parts store can scan the computer for trouble codes for free in the hopes of selling some parts. Once you get the codes you can research them online to point you in a direction to troubleshoot.

take it to the mechanic who put the pump in and tell him to fix it....
Theres a return line and a vent line ...that will cause an odor if disconnected... These should have been delt with as a fuel pump replacement issue... and should be covered by the installation tech who did the job.

stop"topping off" if thats what you are doing. also it could very well be a broken o ring on the fuel tank at the top. has the vehicle been repaired recently? if not it should be looked at by a qualified professional. this is something that should be looked at right away you dont want to have to put a fire out. they are not fun.

A burning rubber smell under the hood might be just that - consider having your accessory drive belt inspected, as it is possible that a bearing in one of the accessories (alternator, power steering pump, air conditioning compressor, etc.) or in the tensioner mechanism might be failing. This sort of fault will often cause that particular accessory bearing to spin less freely than the others, and as a result the belt continues to pass over the associated pulley at the same speed as the engine. Essentially, the result is similar to a car spinning its tires on dry pavement - and a similar 'burning rubber' odor is the friction and heat of the rubberized belt.

If the odor is more like burning oil than burning rubber, the rear valve cover gasket is situated in a place that results in dripping oil, even small and unnoticable amounts, onto the exhaust manifold that is directly underneath the valve cover.

These two items might be places to start your inquiry. Best of luck to you!

well it could just be the transmission modulator it might be faulty or the modulator might be leaking fluid into the vacuum system, or the transmission filter (A/T) might be clogged or dirty

The smell of hydrogen sulphide used to be a side effect of catalysed engines before low-sulphur oils and fuels replaced the old-fashioned stuff.

The sulphur smell could be significant and mean either you have some dodgy fuel or maybe the engine is has too much fuel going through it and if it is misfiring there will be unburned fuel entering the cat.

Most acceleration misfires are caused by ignition faults so I suggest you begin your fault-finding by ensuring the plugs are good and the spark each receives is a powerful quality spark.