EUSS application for EU baby

Hi everyone,

I was trying to find similar topics/timelines but to no avail.

My EU husband and I (non-EU) both have pre-settled status in the UK. Our baby was born in the UK mid March, we applied for her EUSS as soon as we got her EU passport with her EU passport. We linked her application to the EUSS number of my husband.

Several questions that I have:
1) It's now been a month since we applied - we did not get anything from HO. When I called EUSS resolution centre I was switched to the pre-recorded message saying "sit tight and wait". Any insight for the timelines for EU citizens? Can it take longer because she's a baby and won't have NINo?

2) Unlike for both myself and my husband, we did not receive COA for our baby. We only got "Application Submitted" email. Is that a change of process?

3) I assume while we are waiting we are still fine to use NHS (I read somewhere re 3 months for newborns)?

4) Does someone (EU) have experience of travelling out and back into the UK after 30/06/21 while their application is pending? Will we have any issues with the baby?