Nowadays, most schools are very strict at the time of enrollment to 1st standard about the age criteria. In India, most schools follow the KV age guidelines. The admission age slightly varies from state to state. For instance, the CBSE has no prescribed age BUT the student should meet the state or union territory recommendations. (http://www.cbse.nic.in/faq/FAQs_2016.pdf).
The minimum age for admission to I standard is 5 years on 31st of March in the year of admission.
Your son's date of birth is 30th March 2013. He would be eligible for the 10 th board in due time.
The minimum age for admission in X std is 14 years as of 31st March on that year.
Your daughter's date of birth is 21st Jan 2008 and she is in VI std, she would be in X standard in 2022. Going by her date of birth, she would be 14 years in 2022. So, it should be fine.
For admissions under RTE , the rules keep changing, the minimum age for 1st std was 5 years(2015-16), 5 yr 2 months(16-17), 5 yr 4 months(17-18) and 5yrs 8 months this academic year.But this exempts the older students already in the system. (https://timesofindia.indiatimes.com/home/education/news/education-dept-fixes-age-for-std-i-at-5-years-8-months/articleshow/62546285.cms).