I have an old john deere 4020 diesel and on the right side of the tractor where the brake lines go into the case there is a small plastic line that looks like a vent line but it leaks hydrolic fluid??? is this a weep hole for the hydrolic pump or a vent for the case or does the line need to be run back into the case?

SOURCE: '07 5403 John Deere Tractor lift arm will not lower

some-times the 3pt linkage can go past the top position.

When this happens - you will need to force! the linkage arms down.

SOURCE: 2020 john deere diesel tractor with j-d 36# loader

Sounds like you need more hydraulic oil - Or like you said the transmission screen (dirty).
Where it is ??

SOURCE: 3020 carburetor ? john deere gas tractor, 3020

those carbs are real simple you will not have any problem

SOURCE: I have a john deere 430 garden tractor diesel.

Sounds like the fuel pump stoped working.

SOURCE: If I have a small leak on one of the injection

check each injector in turn ( crack it open where the fuel pipe attaches to the injector ) be very carefull you dont get injected ( VERY BAD ) and use a rag to ensure the fuel spray dosent go everywhere , listen for the engine note changing, if it does on each pipe/injector nut this indicates your injectors are ok ,the fuel system maybe drawing air/loosing pressure so then replace your fuel pipe olives which cost pennys and the copper washers on the various banjo bolts /unions