The rights and status of EU citizens living in the UK will remain the same until 30 June 2021. If you apply to the EU Settlement Scheme successfully, you’ll be able to continue living and working in the UK after 30 June 2021.
Any children born in the UK after you’ve got UK pre-settled status will be automatically eligible for UK pre-settled status. They will only be a British citizen if they qualify for it through their other parent.