Is it possible to install a gas engine kit on the bike's existing speeds? Such as with electric assistance.  I'd like to install a gasoline engine kit (because electric ones are wildly expensive) on my bicycle, without the sprocket:  I want to attach it to the existing gears, because I would then be able to shift through the gears to increase/decrease speed as I wouldn't with a 48-tooth/32-tooth sprocket.  I have not been able to find a kit that will place the chain on the right of the bike, where the gears are.  Is there a kit that can do this, or is there a way to fadangle a normal kit to run through the existing speeds?
Generally speaking, no.
A liquid-fuel engine wants to turn a lot faster than a cyclist would turn the cranks.  That's why a retrofit engine often has a small drive cog and an enormous cog on the rear wheel, to decrease the revs and increase the effective torque.
The optimal speed of a small capacity liquid engine is somewhere between 1000 and 2500 RPM.   A cyclist would do 60-90 RPM on the crank, with 120 being possible-but-abnormally high.
If you want a motor bike, its often cheaper to buy a 50cc motor bike and leave your normal bicycle unmolested for riding.
Also, if you remove the ability to pedal, then your ride becomes a motorbike no matter what displacement limits you're under.

Additionally - these liquid engines cannot generate enough torque to pull away from stopped.  So the rider has to pedal up to a minimim of 10-20 km/h and then can release the clutch.  Trying to start a small displacement motorbike from stopped is impossible without stalling.
You need the pedals working to get them moving.