I dont know about the heater issues and the gearshift light. As for the bouncing speedometer could be a loose connection at the back of the instrument panel where the cable connects or possibly a worn drive gear in the transmission. For dash light the battery/charge light and oil shift light are doing exactly what they should do. Cant remember bout the check engine light but I believe it is also functioning correctly as all it does when you first turn the key on is a bulb check. For the light behind the mirror only illuminating when the passenger door is open it may be an issue with the switch that is uses to sense when the door is open is faulty. Easy test is to pull it out and directly ground it and see if the light lights up. And for oil the recommended oil is 10-30 for temperatures above 0 degrees Fahrenheit. I personally only use full synthetic oil and that is what I believe is generally suggested by the majority on here. If you do a quick search for engine oil you will find several threads about it.