Hi Guys - long time family researcher, but new member; go easy on me

I'm looking for some help and pointers in my journey to find my Grandmother real family. She was Peggy Richards. I hope my quick summary of my journey doesn't bore you! The questions are at the bottom

My Grandmother on my Fathers side was reputedly adopted. She would have been born c1915, and passed in 1964 with few stories passed on, and unfortunately was an only child so no family (and no extended family from the adopted side - certainly none now with stories to tell). So the only real source of this information is from my dad (now 80) who claimed it as fact, but the memory is hazy about how he knew this (he seems to think she had adoption papers, but I think this might be unlikely)
I always believed this claim to be true because from composing her family tree I saw that Peggy's adopted Parents (Frank Richards & Florance Hale) only had Peggy and no other children. All other family members around this time were knocking them out weekly, so I wondered if Frank & Florance couldn't have children so adopted one. I could also find no birth record for my Peggy, so was certain that she was adopted.
Anyhoo - Fast forward to when Ancestry DNA started to become a thing. Both I and my Dad carried it out, and it became apparent that there are zero connections with other Richards, Hales (or any branch) so not only was Peggy most certainly adopted, she was adopted completely outside of the family
After finding out for certain that Peggy was adopted, I've been keen to find out (if possible) that line of the family. That's not to say I have lost interest in her adopted side as I still see that as part of my family story of course
So have looked for any clues in any records, and found none so far. However, DNA gave me my first "Eureka" moment a couple of years back. I mapped out my and my dad DNA relations and isolated all those linked to either my own mum's side or my dad's personal side. I then went through those with no apparent connection to my other lines (but with a strong DNA connection) and grouped those who had links with others (shared matches) to see if I could find family. And I got a hit on one of these groups; this group had 12 trees in total, with 8 trees linking back to a "Francis Clare (1810)".
My next task took a while - I basically mapped out the entire Clare family from Francis Clare onwards. As I added spouses I searched the DNA database to see if there were any hits, and eventually, I got one. Henry Clare (1840) was married to a Charlotte Seabrook (1842) and I had somebody with a DNA match that related to Charlotte Seabrook
So I feel like I'm getting close, but then I hit a brick wall. Henry & Charlotte emigrated to New Zealand somewhere between 1865 & 1866. they had one daughter in the UK born in 1865, Charlotte Clare, but fair to say that she went to New Zealand. I think there are 5 Children in total
The problem is I'm finding it really hard to find anything records in New Zealand to help try and trace the family to find the next link. Peggy could be the daughter of one of the 5 Children, but think it more likely it is one more generation, and simply can't map that out
So questions;
1. What route(s) can I go through to better map the New Zealand side of the Clare Family
2. What else can I look into that can possibly help find information on my Grand Mothers blood family. My dad suggested there were adoption certificates, but would this have been true in 1915?
3. Is there something I'm missing in the Ancestry DNA results I can use to better navigate the results. I'm finding it really chunky, and annoying that I can't better search it
4. Any Help at all really!
Thanks Guys