Used cooking oil is subject to pretty much the same issues as motor oil, plus it is more viscous and solidifies at common temperatures. There's lots of people running diesel engines on waste vegetable oil (another name for used cooking oil): http://www.google.com/search?q=wvo
They have to start and shut down their engines on dino-diesel and have a secondary fuel system that they switch over to once it's running; the secondary system heats the oil so that it can be turned into the "small tiny droplets" by the fuel injectors and be used as automotive fuel. Some day, I hope to run such a system.
Rudolf Diesel originally designed the diesel engine to use coal dust as a fuel. He also experimented with various oils, including some vegetable oils, such as peanut oil, which was used to power the engines which he exhibited at the 1900 Paris Exposition and the 1911 World's Fair in Paris.
The fan at the tail pipe suffers from the same issue as the turbine -- it's still not free energy. Also, the fan is only going to have a very tiny output.
Don't get discouraged, though...keep trying to think outside the box, and keep the ideas coming.
or a small computer fan the ones that go on your processor at the tail pipe.
You want a metal fan. I once stuffed my exhaust exit with a few of those plastic whistle things that just have a spinning disc in them and I got maybe 3-4 seconds of idle and like 2 short revs before they melted and quit working.
Good for some laughs tho! I don't see why a turbine in the exhaust isn't viable as a solution. Go pickup a junkyard turbo and rip the compressor off of it. Take the compressor and use small timing belts and gears to reduce the turbine down like 10-15:1(but make sure you can change the gears because this might not be what you want)
Your normal automotive stock turbos only really spin up to 75-100,000 rpm.
I like the idea of using exhaust gases as a turbine. It works for forced induction, why not put an alternator on there instead? Geared properly of course, as 120,000rpms is ...excessive for power generators.
The other idea I'm not so sure about. Burning oil only increases hydrocarbons in the exhaust, as well as gumming up the works. current engines don't burn oil too well. I think your other idea is more practical, and forward thinking.
That sounds like it would be a really good addition for hybrid vehicles to help recharge their batteries faster