RE: propane weedeater engines in planes?
Anything is possible if you want to bad enough. The propane cylinders those things use are pretty heavy though. Maybe some sort of smaller, aluminum cyclinder would work better.
Like Minnflyer pointed out there is a lot of work involved with making it work. I have a 30cc 4-stroke powerhead for a string trimmer that I was going to convert for fun but decided against it.
I also doubt that the performance would be as good as a comperable displacement purpose-built RC gasoline engine.
If you want a cheap gas engine, look at some of the Chinese stuff out there right now, not bad considering the price.
Of course it isn't always about practicality. Sometimes tinkering and having fun is nice.