change the speed sensor and that should fix both of your problems
poor performance
It can make the engine run so poorly that it seems like the transmission has problems.It can make the engine run so poorly that it seems like the transmission has problems.
Makes it hard to start and run poorly.
The engine will turn over , but either run poorly or not at all
Poorly designed and manufactured foreign junk!
The engine could stall when you are on the road, causing a traffic problem.
yes it has to do with timing
The engine would be running poorly and the check engine light should be illuminated with related codes.
Can? Yes, but should you? No. The thermostat is an integral part of the cooling & emissions system. The thermostat allows the engine to reach optimum operating temperature very quickly which is a good thing. Without a thermostat the engine will take much too long to reach this temperature and in fact it may never reach it's correct operating temperature. Engines run poorly when cold. Once the engine reaches its operating temperature (generally about 200 degrees F, 95 degrees C), the thermostat opens. By letting the engine warm up as quickly as possible, the thermostat reduces engine wear, deposits and emissions. The engine will get better mileage and last much longer. Install the correct thermostat and forget about leaving it out. There is no good reason to run an engine without a thermostat.
The catalytic converter
I would test the temperature sensor first. Then have the car scanned.
Either it will not run at all, or run very poorly. Either is likely to do severe damage to the engine.