Is the low coolant light coming on at all?
Gas gauge not working could be the sending unit. Also, check fuses and see if there is one for this.
When you replaced the pump and thermostat and then flushed/refilled, did you bleed the air out of the system properly? It sounds like you may have some air trapped in the system. These cars are notorious for this and can be a pain to bleed. Try this:
Get car up to full temperature in Park. Take a look at the thermostat housing. There should be a small brass screw on top of it. With the car running at full heat crack this bleeder valve open until you get coolant running out of it. If there is air, you should see it sputter out the cooalnt. Once you get a steady stream of coolant close the valve and take it for a drive. Then come back and do it again. Then once done here let it cool down completely and top off the radiator and coolant resivoir as needed.
The pulley shaking should not cause the car to loose power, but you should have it replaced as it may throw the belt eventually, thus leaving you stranded. I would suspect a bad/worn O2 sensor as it sounds like when the car goes into closed-loop that the issue occurs. Also, clean your MAF.
Is there a CEL on at all?
Also, Welcome to the site! If you have any other issues/questions post them in the General Tech Discussion section to get the best response
