I think wizzwizz4 only corrected the (quite big) factual problems of the grandparent. But about the claim of “the vaccine can modify our DNA”, I think this reply is great: https://news.ycombinator.com/item?id=27467454
Basically, while there are known mechanisms for mRNAs to getting converted to DNA, these quite complex mechanisms don’t just exist there. And the mRNA injected gets destroyed in ~half an hour. Basically, if there would be a constantly working mechanism for converting mRNA to DNA, our genome would constantly grow significantly since all sorts of mRNAs are constantly created inside cells.
Setting the technical issues aside, what's the bottom line? I think OP's general point was: "This is not dangerous in the way some people believe it to be dangerous".
Do any of your corrections change that outcome/conclusion in a meaningful way?
(I'm not asking to call your comment into question, but because I don't know how to adapt my understanding based on these two comments).