Model 600 series
First of all, congratulations on a fine pair of carbines. Now, for some answers. Claw extractor, left hand, no, not a model 600. All 600 series (660, Mowhawk 600) were push feed, identical to the Rem Model 700. All had the "dogleg" bolt handles. I have seen a couple of rifles where the bolt handle was replaced. One even had a mannlicher "butter knife" bolt handle.
As far as powder for the .243, remember you are dealing with an 18.5in (or 20in - Mowhawk) barrel. Slow powders may give fine accuracy, but you don't have enough barrel for these powders to get all the way up to speed. Also, muzzle blast is something to be considered. Generally, medium burning powders will give you all the velocity you are going to get out of one of these short carbines.
Accuracy varies, abut generally is pretty good for hunting. Remember what these light rifles are for. If you get great groups, fine. But don't expect alot. The light barrels (with the rib) tend to "walk" as they heat up, sometimes rather badly. This is a game rifle, and 3 shot groups are usually fairly good.
Note, if you disassemble the rifle, take care to get the magazine box fully seated in the reciever when putting it back together (it likes to pop out a little). If it pops out, and you don't notice it, you can bend the triggerguard/floorplate (plastic) when you tighten the screws. I have seen several M 600s like this.
Again, congrats. The little guns carry well, and handle like a dream.