What is the probablity that SARS-CoV-2 will mutate?
I don't see how you want to prevent mutations - and these don't have to be a bad thing as the mutation of SARS (the original one from 2003) shows, here the mutation (or better the deletion of a part of the viral genome) led to an antenuated pathogenic virus. Since this mutation happened in the early phase of the spreading, it became the major virus. See reference 1.

Mutations are a statistical process which happens all the time, especially for RNA viruse due to errors in the polymerases (see reference 2). So the answer to your first question would be: 100%. It is mutating, which can also be seen in the sequences which have been published so far. The differences are only minimal with a sequence homology between 99.91 and 100% (see reference 3), but this can already lead to changes in the amino acid sequence. You can see this in the screenshot from phylogenetic tree of all sequenced SARS-CoV-2 viruses on [Nextstrain] (see the site for the actual development):



To your question 2: You cannot really predict where mutations happen and which will come through in the long time, as this is a statistical process and the sheer number of viruses around in each infected patient. But there are positions which are more prone to mutations, while mutations at other parts of the sequence will lead to much less fit virus. There is not so much data available yet (remember that this virus is only around since the end of last year), but reference 3 has some data on it (figure 3):



Question 3: I don't see how this should happen, as this involves the polymerases which are involved in replication. 

References: 


Attenuation of replication by a 29 nucleotide deletion in
SARS-coronavirus acquired during the early stages of human-to-human
transmission
Why are RNA virus mutation rates so damn high?
The establishment of reference sequence for SARS‐CoV‐2 and variation
analysis
On the origin and continuing evolution of SARS-CoV-2