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When she married she was the daughter of "the late John Smith" in the newspaper:
https://paperspast.natlib.govt.nz/newspapers/AS18910103.2.35.1?items_per_page=10&query=%22Mary+Catherine+Smith%22

Roy Townsend New does appear in Canadian archive as a home child, sent in 1920 by National Children’s Home.

The records might be held in local archives but there should be some info available about Roy, and possibly about Fanny, that mention Albert, as the location of the father/husband was often of interest to authorities (from the point of view that he should be paying for them if he was around).  If you're lucky they'll say something about where he was, or at least give you a better idea of when he left the area (if he did).

As to the Smee marriage - Albert James New and Maude Louise New are on the census togther in 1921 in Reading, so unless your man added 10 years to his age and a new middle name, not him.

It looks to me like Nurse Lloyd published a great number of similiarly worded notices for children born within her hospital - it may not have been driven by Lena or her family at all but simply a service provided (probably also a form of advertising for the nurse)

https://trove.nla.gov.au/newspaper/article/58000944?searchTerm=%22Nurse%20Lloyd%22
 - see here, 7 birth entries in a row (including Dyer)

She also advertised at times for foster/adoptive parents, so may have been the one to organise a placement
(just a couple of examples):
https://trove.nla.gov.au/newspaper/article/27603101?searchTerm=%22Nurse%20Lloyd%22
https://trove.nla.gov.au/newspaper/article/28168483?searchTerm=%22Nurse%20Lloyd%22%20%22baby%20girl%22

Officially, for an illegitimate birth at that time, the father would have to accompany the mother to have both names on the certificate (at least in England and Wales).

Who was the informant in this case? The mother?

It was quite common to see falsehoods, because there was no requirement for documentary evidence to register a birth. Occasionally they turn up in court records.  Usually these involve just saying you were married to the father, or perhaps making up a husband/father out of whole cloth to avoid having that blank space.