It is legitimate to be concerned about the safety of the bat flu vaccination. SEE:
https://www.unz.com/mwhitney/the-covid-19-vaccine-is-the-goal-immunity-or-depopulation/

1. Instead of 10 years of safety trials, there is only a matter of months for covid-19.

2. There are dozens of companies coming up with vaccinations all over the world, and twitter will ban criticism of the safety, without knowing about any every manufacturer.

3. Why the frantic demand over vaccines for kids when healthy kids are not threatened by the disease?

4. Several FDA members would not vote for approval. What do they know? Why do FDA members need to be rushed?

5. Instead of being a normal vaccine where a dead virus is injected, the coronavirus vaccines will be based on a new method of mRNA that is not as well known.

6. The people screaming about having to rush the vaccine have a pattern of lying as in CNN.

7. Robert Kennedy Jr. said that over the past 30 years coronavirus vaccines make people sicker. They could not get it to work for 30 years, but now all of the sudden they can do it?

8. Proponent Bill Gates is a con man. See cartoon below.

9. Why push the vaccine when such a high proportion of people already had it?

QuoteVaccine development is a long, complex process, often lasting 10-15 years
https://www.historyofvaccines.org/content/articles/vaccine-development-testing-and-regulation

In answer to your first question, it was expedited by President Trump. He deserves full credit for getting the vaccines by Pfizer and Moderna approved in incredible time.
IIRC, children will not be vaccinated until the safety and efficacy for children has been fully proven since, as you say, they are less affected for the most part, by the virus. Children sometimes react differently than adults. The adult vaccine has met all of the safety and efficacy criteria required for public distribution.
RFK Jr. has a history of promoting anti-vaxxer propaganda.
Bill Gates is a big boy. He can defend himself.

Are you aware of the Nigerian lawsuit against Gates for crimes against humanity?  Gates uses African children as his lab rats.