68 tranny/engine probs

Hi,

first of all id like to introduce myself as i am new to the forums. my name is tommy hutson. but here we go. the shifter on my mustang is a little funny. it doesnt stay locked in some of the gears and it is hard to get the car to switch into drive and reverse. also the car drives in neutral. is this a problem with the shifter or what. another thing is. the engine gets very hot with only mild driving. i have pretty much traced the problem down to the water jackets on the car probably being kinda dirty. is there any way i can clean them out with some kind of cleaner that i can run through the car for a bit then get like a backflush kit or something. I plan to flush all the radiator fluid out. but i am not sure as to how to get it all out. what kind of radiator coolant do you guys recoment running. one other thing. the battery keeps killing itself for some reason. its a fairly new batter and the alternator is brand new. when the batter dies and i go to try and start it the belts sign goes on on the console. i am not sure what this means. could it be a short somewhere draining my battery? thanks to all who help.

thanks,
tommy

okay thanks guys ill take your advice.

Thanks Again,
Tommy

an update. I flushed the radiator with prestone supercleaner or whatever and water. and jsut kept flushing it and draining it after the 3 hours that the cleaner recomended. the car is runnign a hellof alot cooler now but it still gets a bit hot while idling. i suspect that a fan shroud and maybe a better fan would help here. I fixed the shifter. the neutral start switch and linkages were out of wack so all i ahd to do really was mess with it and figure out how the things work together and fix it like i thought it should be. shifter is alot better now and is actually in drive when it says so lol. but besides all that i still ahve problems with my electrical system. my car drains the battery when im driving. i took the car down to autozone a while ago and had the batter tested and alternator tested in the car while running. both seemed to be good. we replaced the voltage regulator and saw the voltage jump from 11.2-12.4 which i found to be a significant improvement. however, i still am not very confident in my cars starting abilities. after id say 6-7 starts. the engine doesnt wanna crank over anymore. Now I dont know but i was reading somewhere that having a timing that is advanced too far will hinder starting abilities. so i got in with the good ole timing light and found out she was timed at about 11 degrees advance. specs say 6 is factory so i retarded the timing a bit. not only is the car idling better but its running a bit cooler also. I havent had any problems starting for the rest of the day trying to start my car. do you think that its possible for the hard starts because of bad timing to cause my battery to die like that. ohh well only time will tell i go out and try and fire her up tomorrow morning and weel see what happens. thanks alot for all the advice guys.

Tommy