86 celica problems

hi..i just purchased a 1986 toyota celica gt..beautiful car, no rust on body or chassis, interior has no tears, not even a crack in the dash...it's a 5 speed...but it has 2 problems i don't like...after driving for around 20 minutes, it will just shut off..no raise in temps or anything...just cuts off...i was told the catlyatic converter could be clogged, or the return line for the fuel could be clogged/pinched, causing a vacuum in the tank...that is the main problem any suggestions?....also...it shifter very hard...not going into gear or anything...just moving the shifter in neutral is hard...like it is rusted...maybe some wd-40? any suggestions on either problem would be excellent...thanks...adam...and also...can ya direct me in the area to find parts for it...like performance, styling, etc...

Cat could be to blame for stalling, should get it fixed before youb drive it any more. There is grease that need to be put in the base of the shifter. Also when was the last time the gear lube ion the manual tranny was replaced??