Vlad,
In the 3rd photo there appears to be 2 areas on the heel that have either tape residue or the finish is missing and the finish on the toe is scuffed.
Just a touch up of these 2 areas to protect the wood is all it needs.
The dents and dings are its history and in my opinion should not be removed.
Igorrock is correct with the accraglas buttplate repair.it works very well.
You have a very nice rifle there. I am envious!