TNNAROOT's first project - a pusher trailer
I see no one has replied in the several days since your post. I think it's because it appears you might need more help than can be reasonably given online. I think you should do a lot of reading in this forum before you start collecting parts. I notice you have been advised of this before.
Apparently you don't have a chainsaw engine yet. If you got one, it would most likely have a clutch on it. Chainsaw engines can be used, but their clutches are designed for a cutting chain not a roller chain. You would have to modify the clutch by replacing its sprocket or perhaps find a clutch to fit that works with roller chain.
It is probably more difficult to attach a throttle cable to an engine that has a trigger, but maybe not if you remove or bypass the trigger.
A chainsaw doesn't have the typical bolt holes for attaching it to your trailer. I'm sure that can be solved, but it is just another headache that will be difficult for a first time builder.
In a previous post you replied that you have a 2HP 2 stroke engine. Is it from a chainsaw? Can you tell us more about it? Can you post a photo?
It will take a little research to find a sprocket for that wheel. The bolt pattern must be accurately measured unless you have the catalog description of the hub. You will need longer wheel bolts and spacers on each bolt to position the sprocket correctly.
You will need a long bolt of the proper length and diameter to serve as an axle and spacers will be needed there too.
It would be best if the wheel had 'high-speed' bearings.
You have to decide on a gear ratio which will depend on the RPMs and horsepower of the engine primarily. It will also depend on the type of riding you want to do and how hilly your area is. Your gear ratio will determine what size sprocket you need on the wheel and will also depend on how many teeth are on the clutch sprocket.
It would be much easier to make a pusher trailer with a Briggs or similar horizontal shaft engine around 3.5 to 5 horsepower. You could use a minibike/gokart type centrifugal clutch that fits the typically 5/8 in. or 3/4 in. shafts of this size engine and #35 chain. These engines are low RPM engines that allow a direct chain drive from clutch to wheel. A typical ratio can easily be obtained with these components by using a wheel sprocket that is about 2/3 of the diameter of the wheel. A chainsaw engine will probably be a much higher RPM engine that will require a jackshaft to get a useable gear ratio. Your best bet for a first project would be to use as many parts as possible from a simple minibike. Use the search function to read all you can about pusher trailers in this forum. I and others have written about our builds. I've written several posts about my pusher which is the simplest of all I've seen. Here's a video:
http://www.youtube.com/watch?v=XjEgsKqfi74