EFI stands for Electronic Fuel Injection. TBI (Throttle Body Injection) is one form of EFI, as is SMPI, MPI, etc. All Germans shepards are dogs, not all dogs are German sheapards.
1. If it idles poorly when cold, then you can rule out most of the EFI sensors. They don't kick into the mix until the engine warms up to about 135*F and tell the computer to start leaning out the fuel mix. It's like a choke on a carb, you enrich the mix till the engine starts and lean it out as it warms up.
2. I thik you mean 1k (1000rpms), right? This is a very high idle for the engine, with a 5 spd it should be closer to 750rpm. Does the RMP climb as it warms or have you manually jacked up the RPM?
3. The K&N Filter should give it better breathing. The O2 sensor still is able to work with the better breathing. I don't think that's an issue. If you feel it is, take the filter off and let it breath freely. If the filter is choking down the engine then you should notice a difference.
4. I'd be more inclined to think the problem was one of a common tune up like Plugs, Wires, Cap and Rotor, etc.
5. Have you pulled the plugs to see what they look like? Anything out of the ordinary such as deposits, etc. on it?