Are STOP codons impacted by base insertion or deletion mutation?
Yes. Mutations can affect STOP codons and they do relatively commonly. These are important because they can lead to significant changes in the resulting peptide and are likely to affect protein functions or phenotype.

For a point mutation (a single base substitution), there are several possible effects:


silent mutation is a synonymous base substitution which does not change the encoded amino acids (this is neutral variation).
missense mutation is a non-synonymous bass substitution which changes only one amino acid in the protein (these can affect protein functions but do not always).
nonsense mutation is a change in a coding codon to a STOP codon (this truncates the encoded amino acid sequence prematurely resulting in a shorter peptide).
nonstop mutation is a change from a STOP codon to a coding codon (this means the amino acid sequence will continue to the next STOP codon resulting in a longer peptide).


Insertions and Deletions in DNA sequence (InDels) are important because they change all codons that follow it (not just the base substituted):


frameshift mutation adds or removes a base which resulting in a change in the reading frame: all bases following will result in new codons, including STOP codons (this commonly results in entirely new protein domains and proteins of different lengths as STOP codons will also be changed. They are encoded in the reading frame like all other codons.


As you can see, mutations which affect STOP codons are very important as they drastically change the protein sequence. This usually disrupts the protein function and causes diseases or inviable embryos. Most of these are removed from populations long-term by natural selection. However, it can rarely lead to entirely new proteins beneficial to the organism and evolutionary changes. This is more likely with duplicated genes where one can change while the other retains the original function. 

As such, mutations involving STOP codons are among the most biologically important.  Another important case is splice functions. Point mutations and frameshifts can also affect intron-exon boundaries, resulting in new splice variants, skipped exons, and reading further into introns (which may contain splice junctions or STOP codons).