Claiming UC, Childcare, Maternity on ILR and wife on spouse

Hi, I know this has been asked multiple time but please bare with me.

I am on ILR wife on spouse- I claimed UC last year for 2.5 months (of course if was a combined account) but they refused my wife as she does not have access to public funds. MY QUESTION:

1. Do i need a letter from DWP saying that my wife was refused and I was the only one claiming?
2. How can I get this letter as I want to apply for her extension.

My wife also claimed maternity - medicines for free. MY QUESTION:

3. The Maternity certificate is valid for 2 years. Is she eligible to claim for the complete 2 years and is this
allowed - no access to public funds

We are about to send our 3 month old baby to nursery due to circumstances, MY QUESTION:

4. Can I claim benefit for my baby (this is not 30 hours free). This is where the government will pay 20% towards the nursery charges as the account will be setup via gov.uk?

5. Will any of the above impact my wife's spouse visa Extension?

Please Advice