Leaking drain trap.

Two questions.....
1) I have installed a new drain trap under the kitchen sink and the difference is that the cones do not seat sufficiently between the new trap and the main drain pipe. It seems that there are two slot openings in opposite sides of the ring nut where the small flanges in the trap prevent the ring nut coming off the trap itself.
Without changing the main drain pipe, which would be difficult based on the location under the sink, is there a way I can seal those two openings to plug the leak. I can remove the trap, so what I would like to do is remove it, drain the water, connect the trap back again then apply a sealant where it leaks. What is the best sealant to use to stop any more leaks?

2) I also have a leak where the pipe from the disposal connects to the Tee with the baffle in the main drain. The pipe has a flat plastic gasket, but I cannot tighten it up enough to seal the leak. Should I place a rubber washer between the two surfaces?

I suppose I could continue to keep tightening, but I am very leery abot over tightening and causing the nut to crack. It has happened to me before which meant going out to purchasing extra parts and redoing the whole thing again.

Any advice would be appreciated.

Apply pipe dope on the washers, see if that solves the problem.

Nothing I did would fix the trap leak. The difference between the white pipe material, vs the black not having the cones match was the issue. I finally broke down and cut away the black pipe to the wall and using a sleeve coupler added the matching white pipe and elbow connection to the trap. That fixed the problem. Why is there such a matching difference between the black (ABS?) material and the white (PVC?)

The leak from the disposal pipe was fixed by adding a rubber washer between the two surfaces, and using a pipe sealer.
Everything is hunkydory again. Thanks.

leaks

The is usually no "difference" between ABS and PVC, nor do the seals require a plastic and rubber washer, nor is a joint sealer required. Therefore the supposition would be that there was a functional problem with the installation rather than with the materials.