The jagged tool is... well a jag, wrap a cleaing patch
around it to prevent the tool metal from scraping the inside of the bore.
As you pointed out, the Brush is obvious, it can be bent, so be careful with it.
It can be used for the chamber and the muzzle.
The fat end of the tooth pic type tool can be used to lift the gas block lever (notice the little hole), and it can be used to help your finger lift the receiver cover lever. I like to wrap it in a few cleaning patches and carefully use it to get into the nooks and crannies.
Since I don't have a cleaning manual I'm pretty much guessing at what else these tools were used for on the carbine.
OK since it is a slow day for me I ran down to the gun room and took some pics...
How the handle goes together, feed tool into big hole, through the hole in the cleaning rod, exit small hole in the handle.
Slide muzzle protector down rod, then screw on the cleaning brush or jag...I use the brush first.
Cleaning from the muzzle end with cap in place, you will notice that it locks in place with a twist.
How to clean the chamber with the brush and rod, remove muzzle protector cap to do this.
Notice the grove in the receiver...pretty clever IMHO.
Also note that some russian kits had extra parts...like a mini flat head screw driver like the AK tool kits etc.
The SKS kit shown is an early Chinese version.
PS when taking the tool kit out use your finger on one side so the door doesn't catch your finder nail...kind of ouchy.

Some use the cleaning rod for this as well, but that might scratch the trap door metal a bit.
I hope this helps some what.
PS Also check youtube as there might be something posted on this topic on there by now.