You can dry fire it, but limit it as much as possible.
If you take out the bolt from the bolt carrier, you will see the face of the firing pin, it is just a small piece of flat metal, and you are hitting it on its edge.
The bolt hold open is manual. Some ranges require the use of a hold open so they added it as a selling feature.
Most aftermarket magazines; all for the Saiga, have the feature for a bolt hold open after the last round.
If that is the feature you want, then just buy an American made Saiga replacement magazine.
Look around, there are several versions of stock sets available.
Many are quite cheap to buy. Less than $100 is common for simple sets.
There is even an adapter that can be purchased so any AR stock can be used on your AK. Going that route, you can use the empty recoil buffer tube as storage space, or to add a damper.
Google is your friend.