ad 1) - Illness is called covid-19, virus is callled SARS-CoV-2, thus SARS-CoV-2 might mutate. Still should stay covid-19 like cold stays cold and flu is still called flu despite mutations

ad 2) - There already are some vaccine candidates, but it takes a long time to properly assess effects on humans

ad3) No, no vaccinations for kids for flu or common cold are administered; almost everybody will catch covid-19 within one year according to the UK and German governments, kids have usually only mild symptoms and mortality is very low in young age, so no need for widespread vaccinations among kids.