my car drives good until i shut the engine off. when i restart it the gear selector moves through the gears but does not go into gear.(all gear selections act like neutral) it’s a 1994 ford taurus please help

when i start the car it runs for about two to three minutes, as soon as it heats up then the car just stops going almost like it doesn’t have a tranny in it i think its something to do with the pump that makes the tranny change gears can anyone help i have already tried checking the cooling system rad., lines, pump, the tranny is not low on tranny fluid ect. it is something to do with the tranny im sure of that

I sometimes drive a 1987 Ford Taurus station wagon, the automatic transmission slams gears when it shifts. Could a transmission "flush" fix this, or is rebuilding it ($$$) the only way to really solve it? (not worth it because of age of car)