A good combination of parts to upgrade the torque and speed of the Razor Dirt Quad are:
Regarding the batteries you would need to take some measurements and see what the largest size three batteries would fit inside of the Dirt Quad. I am not sure how much space for batteries there is in the Dirt Quad so I can not make a recommendation. The dimensions of our batteries are listed on this page: http://www.electricscooterparts.com/batteries.html
For reverse we have a reverse switch that would work great for the Dirt Quad. It is our item # SWT-715 and is available on this page: http://www.electricscooterparts.com/reverse-switches.html
Here is a gear ratio calculation using our MOT-36750B and MOT-36100B motors with an 80 tooth axle sprocket on the Razor Dirt Quad.
I do not know of any parts
that will make the Razor Dirt Quad go faster which can be bolted on without custom made adapters or frame
The 36 Volt 750 and 1000 Watt motors and their mounting plates are quite a bit larger than the original 250 Watt motor so a custom made adapter plate would need to be bolted onto the existing motor mounting plate, or a new motor mounting plate welded over it or in place of it.
The amount of driving or ride time depends on what size batteries the new battery pack is made with. Since 36 Volt 750 and 1000 Watt motors are three to four times more powerful than the original 250 Watt motor they will draw more power from the battery pack than the original motor does, so the new battery pack would need to be substantially larger to have the same ride time, or more ride time, than with the original motor and battery pack provide.
Usually an adapter plate can be made which will bolt onto the existing motor mounting plate, so that no welding needs to be done. However making an adapter plate out of steel would require some basic metal working tools. If the Dirt Quad will be used in mostly dry conditions then an adapter plate could be made out of a plywood. If making an adapter out of plywood I recommend using cabinet grade wood so it is uniform and easy to cut and drill.
Due to chain alignment issues I do not think that any motor other than the original motor can be installed without making an adapter plate that is either bolted or welded onto the existing motor mounting plate.