Gene
expression is
not the same as mutating DNA. It refers to the transcription of DNA to mRNA or translation of mRNA to protein (often the same term, "expression" is used for both of these processes, so you need to glean the usage from the context). This distinction is explained in any introductory biology course; you should be able to find more detail of this process in any general biology or introductory genetics texbook.
Continuous modification of synapses is normal neuronal activity. Yes, it is involved in learning and memory, but that has
nothing to do with germ line genetic modifications that would be passed onto offspring. Inheritance of acquired characteristics (Larmarkian theory) has been LONG ago disproven. The
ability to learn and for synapses to be modified is due to genetic coding, as gerben qualified previously, but
what you learn, dream, experience, etc., during your lifetime does not alter the genetic code to be passed on to offspring. Even
if (I'm not saying it happens, just a what if scenario) some process in the brain altered/damaged DNA in neuronal cells, that is a
somatic cell mutation, not a
germ cell mutation. In other words, it is not affecting sperm or oocytes, just neuronal cells, thus not passed on to offspring.
(Also, please note, my name is Moonbea
r not Moonbeam. You've made this error more than once, so I don't think it's just a typo.

)