Welcome! They've about covered everything.
The video links may be helpfull to you, i put them up for two reasons;
1/ Most guitar techs have no experience setting Jaguars up
2/ If you feel confident enough it is always better to learn how to do it yourself
The truss rod adjustment has been discussed a billion times and there should be a 'sticky' on it. Usually the only time you need to adjust the rod is if there has been a dramatic change in string gauge you are using on the guitar.
If you keep your Jag bridge the main thing i would advise is lubricate the saddle grub screws, bridge assey screws with vaseline (to stop them working themselves loose) then raise the saddles so that the grub screws are seated in the saddle not sticking out and lastly lower the whole bridge.
The best three ways to stop string jumping is either by using a 'Buzzstop', filing a small slot in each saddle to house the string or get a mustang bridge.
For high gain it is easier, cheaper and quicker to use a processor with a 'gate' and EQ rather than modify your guitar. But if your a traditionalist and want to push a valve amplifier with your CIJ Jag you will have problems with microphonic feedback, so a bridge pickup upgrade will be certain.