With the ride, that's fairly common. If you were to just push down on the padding on the bell with your finger, you would hear the sound trigger as soon as you made contact underneath. Even if you push down slow and steady, you get the sound of a full impact bell trigger. I was thinking about taking mine apart and seeing if there was a way to mod it to get less of a gap in the bell.
With the cymbal edge you also pretty much need a full on strike with the edge of your stick to trigger that sound. I was able to find the sweet spot on mine where it requires much less force, so I positioned the cymbal accordingly. Try tapping all around the edge to see if yours has this also, mine was about 2 inches from the left edge of the rubber padding.
As far as the crosstalk though, I dont have much experience with that. Maybe try testing turning the sensitivity down and seeing if that helps?