I suddenly noticed the speedometer stopped working

While I was driving on freeway about 120 miles away from home, I suddently noticed the speedodometer stopped working, the needle indicated at zero speed (the actual speed was about 60mph). I also noticed the Engine Service light came on. I pulled over, turned off engine and restarted then started driving. The speedodometer started working fine but the Engine Service light remained on.

After driving for couple miles, the speedometer stopped working again. When I pulled over and turned off the engine, then restarted the engine. When I shifted my transmission to "D" anb stepped on the gas pedal, I noticed the RPM meter went up to 3000rpm and the engine sound very loud but the actual car speed is about 10mph. It seem like the transmission still at first gear and couldn't shift to second gear. I turned off the engine and checked the transmission fluid and engine oil; I noticed both are sufficient. I didn't know what to do next and extremely worry, I restarted the engine and shifted the transmission lever to "D" and slowly stepped on the gas pedal. The car started driving and the transmission shifted to second gear and worked normally as if nothing went wrong. I continued monitored the Engine Service light and speedometer until I got home. During this time, the Engine Service light always remained on; however, the speedometer was working intermittently.

I've driven this same car to work for three days (my work place is seven miles from home). The Engine Service light stil remained on; however, the speedodometer and the transmission stop showing problem.

I have two questions:
1) What made my speedodometer working intermittently?
2) Why my tranmission failed to shift then just work fine now?
3) Are these two problems related?

Your answers in great detail are greatly appreciated.

Regards,
Bonsaiee