You don't have to do anything, but remember that you will have to leave Thailand before 31 July if you don't extend your permission to stay. If the borders don't open before 31 July, the amnesty may be extended but there is no guarantee of this. Personally, I would go to Immigration and do your extension if you can, assuming you plan on continuing to study here. Immigration after 31 July will be a scrum!
No one knows. My guess is that a lot will depend on which country you're coming from and the Covid situation there. Mandatory quarantine in government facility will not be practical. I think some flights and possibly the Laos/Cambodia/Myanmar border may re-open next month.
Nobody knows! My guess is that it might once the public holidays are over on 7 May, or from Monday 11 May. There really is no longer any reason why it is closed.
It's straightforward but you will have to wait for VFS to re-open. You can't get a UK birth certificate as the baby was not born in the UK. You just need an authorised translation of the baby's Thai birth certificate. It took me around 3 weeks to get my baby's passport but I fear that once they reopen it will take longer now. The passport is actually issued by HMPO in Liverpool.
Feel free to delete my comment, but my kid has lived here as my dependent (I have a Work Extension) and I have never done a 90 day report for him (he's 5) - and it's never been an issue at Extension time (my wife and I always do ours).