ILR for T2 PBS Dependant with 2 entry clearances

Hi

First of all, it's great to know that there is help available and really appreciate the moderators and members who provide valuable input.

I received my ILR in June 2019 via 5-year Tier-2 route.
I have a query about my T2 PBS dependants - child and wife.

My child's situation is as follows:
Child (born in UK) is 2 years old and on T2 dependant which expires 14 Aug 2019. I was going to extend his T2 dependant visa but having stumbled upon this forum realized that he is eligible for MN1 registration via Section 1(3), as he was born in UK and because I (father) have ILR.
I applied for his citizenship registration and have a UKVCAS appointment for him on 09 Aug 2019.
I believe this is correct, however would appreciate if someone can confirm it just to put our minds at ease.

My wife's situation is as follows:

T2 Dependant Visa (Entry clearance) issued: 22 July 2014 (Expiry date 02 March 2017)
Entered UK: 13 Sep 2014
Visited India in Jan 2015 and returned to UK in March 2015.
Left for India: 09 Nov 2015 to do a mandatory internship.

During that period, In July 2016 when she was in India, I changed my employer and I got new Tier-2 visa. At that time, I was not aware that my wife could still use her existing Tier-2 dependant visa to return to UK (had no idea of this website). So I applied for new entry clearance for her as T2 dependant.

New Tier-2 dependant visa submitted in India on 26 July 2016; however, it was refused on 11 Aug 2016 as TB certificate was missing (my mistake). The rejection letter was sent to her on 12 Aug 2016. So, she re-applied on 25 Aug 2016 with the TB certificate included and application was successful.
New Entry clearance was issued: 31 August 2016 (Expiry date 14 August 2019)

Given the above, the question is - does she qualify for ILR now (01 Aug 2019)?
I was going to extend her T2 dependant but having read the forums, my understanding is that she qualifies for ILR as she got new Entry clearance prior to expiry of previous visa and both were T2 dependant.
Also her absences do not count as both visas were issued prior to Jan 2018.

Would appreciate your input.

You assumptions are correct. Your baby will get British citizenship and your wife is eligible for ILR now

Thank you very much Zimba. Very relieved to hear that.

Just as an update - my wife has been granted ILR.
We went for super priority yesterday.