As for the joint check and extractor, take out the screw in lug and put some penetrating oil such as Kroil or WD 40 in there and try to put a narrow bladed screwdriver in the opening that shows in your picture to see if you can get the extractor to open. If it does move, the joint check will also move, If you get it to move put more penetrating oil in the hole and get it to where you can move the joint check with your fingers.
To remove the joint check turn the barrels on their side with the lettering on the barrels up. look carefully on the right side about 3/32" at around the 4 o'clock position and you should see the outline of a 1/8" dowel. You have to drive this dowel out to remove the joint check, If you can not see it, lightly sand this area going longitudinal with the barrels so that the sanding marks will be with the right orientation when the barrels are being refinished. If you still have trouble seeing the outline of the dowel, put any type of dye in that area and it should seep into the hole around the dowel for you to see it.
If you get this far, let us know and I will tell you what is next to do.