My toyota seems to run fine but intermitently there seems to be a sqealing sound coming from the heater area,and sometimes my battery light flickers on and off but car starts and runs just fine .

sounds more like an engine issue off the top of my head. The transmission runs off the vacuum from the engine. If the engine timing chain is stretched it will run then not run, have problems idling and shifting and won't charge the battery properly. anyone who has done one before could probably tell you just by the sound of the engine running.

Get a volt meter, start your car and see how many volts your car is producing while running. Should be around 14 volts. May want to watch the meter for a while since your electric seems to fluctuate. Most voltage regulators are internal of your alternator. If you are getting a lot more or less than 14 volts while running, replace the alternator. If it is not charging, voltage will drop as vehicle runs, until battery is dead.

misfire check spark coil

it is the belt it is either to tight or not tight enough

It sounds as a weak battery. Try to horn with the head light on to see if it can sound.
1- Have the battery recharged.
2- Clean off the cable terminal really well to prevent corrosion built up causing high resistance. If there is high resistance at terminals, there is not enough current flowing through the starter hence there is no starting.
3- If battery is good after recharged as well as horn could sound, but still not started, then the starter solenoid needs to be checked out. Good luck.

sounds to possibly be a intermitant fuel pump or a bad fuel pump relay. Check those areas. Hope this helps.

Have alternator tested again, seems like alternator has intermitent problem.

sounds like the belts need replacing, also check the power steering pump could be going bad

have the engine wire harness checked maybe a communication problem between modules.

Try your headlight switch. If it is going bad it should affect all of these since they all work of the same switch.