DNA methylation and histone acetylation occur at specific sites called CpG islands in coiled DNA molecules. These processes are modulated by transcription enzymes that respond to catalytic processes that occur in the nucleus of cells all the time to control gene expression. This is why cells make only specific proteins even though they have all the DNA for every possible protein in the body.
The mRNA molecules are prevented from entering the cell nucleus by a boundary and therefore can not have any effect on DNA. The mRNA is transported by enzymes in cell protoplasm to ribosomes where it is processed into COVID spike protein. When this is expressed on the cell membrane it triggers the immune system to make antibodies against the real virus.
Thank you for the excellent description.