The issues that I have seen and experienced with the 3GX are as follows.
3.1 - This version is incredibly stable in the air and adds a few options to the menu setup. However, this version likes to tip over on the ground before take off. If you can do a half spool up and 'pop' it into the air, then it is likely fine.
4 - This version has some weird twitching issues with the tail in the air. It is stable on the ground, but the tail kicks on its own.
5 -This version has an absolute horrible tail bounce back. I had one that had a 180º bounceback. So you would go from tail in to tail right and it would bounce all the way back to tail left.
Do note, not all gyros experienced this issue. Some are fine on 5, some are fine on 4, all that I have seen suffer from tipping over on 3.
As for what ones are compatible with dsmx, I'm not sure. Never dove into them quite that much.
Adjusting the swash to get the correct movements, you will need to go into your servo reverse menu's and adjust the settings until the servos are moving together like they should, even if they are reversed. So collective is working the swash up and down, elevator is working the swash forward and back and aileron is working the swash side to side.
Once you have it there, then you will need to go into your swashplate menu, or may be called swash mix in your Tx, and reverse the ones that need reversing by taking the positive number in that menu and making it a negative number.