Getting rain water behind siding
 

Recently had vinal siding installed, J channel at bottom is about even with top of lower trim board and I think is allowing rain water to run behind that board (can see it dripping) Seems that the J channel should have been lower. Can I do this and how do I extend the channels on the sides? See pic.

Yes you should have had a Z flashing on top of the board and behind the paper behind the siding. You can expose the nails at the top of the first panel with a zipper tool and remove that panel to do this, you will need to cut some off the bottom of that panel when re-installing it so that it isn't to tight.
Zipper tool is a cheep little tool sold where they sell siding.

z flashing?
 

What is a Z flashing and how does it help? Also, not sure what you mean by cutting the botton panel.

It looks to me that you have to remove some siding to install flashing and then the siding will be to big to replace.

I personaly never would have installed the siding the way it was done.
All the old wood has been left exposed. I would have remove it and used vinyl outside corners and ran the siding from the bottom using starter strip.
You need to add that Z moulding or another way is to use coil stock and wrap that bottom area and run it at least 3" up behind the siding.