Mini Stock.

Should I use filler on it?
Should I sand in the mud?

Well, if you desire a filled finish, I would sand in the mud (if I were doing it). I do keep old 35 mm film canisters filled with sanding dust that can accelerate the process.

Sand in mud; I never use filler. I used to, but realized it was literally, colored dirt, whereas sanded stock mud is, wood.

I always sand in the filler. I start with 320 grit & let it dry with out wiping it for the first coat' Then I dry sand it to get it smooth. Then start wet sanding & wiping cross grain with soft paper towels about six times ending with 800 grit paper. When it's done I wipe it with real fine steel wool & put stock wax on it.

I sand in finish that contains filler. I usually sand in every third coat leaving the mud on the first and perhaps the second coat moving it around with my finger then let it dry and wet sand it wiping. then coat with finish every 3rd application. until I like what i see, the coat with thinned finish let dry and polish with a cheese cloth dipped in oil and the compound until I get an egg shell luster or flat finiwh which ever is needed dependent on the guns intended use.

Method is used according to what's working on te wood, Black walnut and European walnut vary a good deal as does California corkwood grown on a ditch bank.

I never use steel wool as minute particles imbed the finish and pop up some years later or sooner

What is the real need for filler apart from getting a glass-smooth finish?

Does it help make the stock significantly more weatherproof?

I think the pores remaining after extensive grain-raising are an attractive reminder of the organic nature of the material and help cut reflections that hunters don't need.

I was worried about a blotchy finish so there is one spit coat of shellac ( 1:1 with alcohol.)

I then sanded it with 400 to get down to the wood. It is very smooth.

I'm thinking walnut danish now.

Yes, never use steel wool on wood.
Yes, if you like the pores remaining on the surface, there no need for filling anything. It is solely cosmetic. Most people like smooth surfaces though.
Never use shellac; it is a poor finish from centuries ago. It is not waterproof. And water will make it turn white.

Yes, fillng the pores makes wood ,more water proof for Petes sake except on the internet..Has for hundreds of years!Helps prevent warpage that causes movement in the POI...

Thanks Ray, I'll take tha Sako when it rains - it's still got the glossy finish from 1980, touched up with oil over scratches.

There ya go!

maybe 2-3 more coats and I'm done. I'm not convinced it's maple or birch.

Birch as a rule but with that grain?? maybe European walnut, depending on which Mauser it came off of..based on the grain flow it could very well be walnut, cross your fingers..It would be nice to start over and use Alkanet root or Mohagany Watco to darken it and bring out that grain better..Hard to be 100% sure without stock in hand..Birch looks like Balsa and seldom has any grain..