well to check the screen you need to drop the tranny pan
undo all those little bolts
and tehn there is a liver shaped piece held with i think one screw
it has an opening on the side you are looking at , as that is the oil pick up and it sits almost to the bottom of the pan ( so it is going to be the lowest thing in there)
undo the screw pop it off and clean it
i used degreaser and a small metal brush to get deep inside as the openings top or bottom are small
make sure it is really dry
no water at all before reinstalling
i can't remember what i said about pick up lines but i think it was regarding flushing the system
it would take a few gallons and a large container to do it at home
but possible
basically getting the car and transmission to normal temp
( see here is your problem when the flow valve opens you car quits)
do a simple flush first of the fluid with a line from a fresh jug going to the tranny and the one that leads to the radiator to a catch container
so it is just sucking up new fluid and dumping the rest right out of the system
i am speaking of the 2 hoses that come from the tranny to the rad for cooling it
this is the easiest and only place i know of to redirect the flow
and may shops have a filter machine ( walmart)
which does the exact same thing
probably for less money and head ache