Here are some responses to your questions. Others can speak up too...
Do you find the boat to be a little tender? I will be sailing most of the time single and double handed, so not much weight on the rail. Maybe some distance races but not planning on any round the buoy racing.
The boat can be trimmed and balanced. If you do not trim properly it is easy to get a lot of helm. There are many sail adjustments you can make on the J/30 to get the shape you want for the conditions. If it is breezy in your area (SF Bay it is!) you'll be using the #3 jib (110%) often. You should rig the reef line and practice using it for the big breeze. That said, if you do sail with full crew the weight on the rail helps.
I'm especially concerned with wet coring and will be looking at that. I noticed some water stains at the chain plates.
The area around the chainplates should be checked to make sure the bulkhead isn't water saturated. It was on Rhapsody and
I fixed it in this post. The area where the chainplates passes through the deck should be dug out and thoroughly cleaned, with new pliable caulk inserted. There is a good chance you have wet core in the deck by the chainplates. This should be dug out and epoxy isolated. It is a very common J/30 problem. If you find a J/30 that does not have wet core, you are extremely lucky. Most every boat I know of had some work done to fix and isolate wet core.
I've looked at three boats now and all have rudders that seem slightly lose in their pintles and gudgeons. I assume this may be normal but, does that drive you crazy after awhile?
It has a stainless on stainless wear surface that bears some load, thus wears. I removed the gudgeon and pintles and took them to a machine shop. The holes were opened slightly, made true round and a marine bronze sleeve machined as an insert to take up the play. You could also use something like Delrin. This fixed the rudder play problem.