1) Why do you think you need a trigger spring? I assume you mean trigger return spring? Basically only M28/30's have this and it was deleted from the M39 design because it doesn't actually DO anything to improve trigger pull, or anything else for that matter. It's a useless mod.
2) If you mean the trigger itself, only a small number of later production Finnish mosins had a 2 stage trigger. If you want one, you can buy them on e-bay but they don't really improve anything, they just change the feel. If you really want a lighter and crisper trigger, that's about fitting and stoning the sear to the cocking piece. On the M39, which was the pinnacle of Finnish mosin design, the Finns changed the sear angle by grinding it to a specific shape and polishing it to reduce friction. You can also polish the cocking piece sear engagement with 600 grit wet/dry paper. Works wonders.
3) Why would you use cork bedding in a Mosin? Mosin receivers can be VERY easily made to free-float the barrel by using flat stock under the receiver at the tang and just behind the recoil lug. Bedding will be finickier and generally less effective. Not every mosin needs any adjustment, I would shoot some groups before defaulting to modifying anything.