Can't say I 'recognise' them but here are a few things I have found.
Firstly - Henry was a little hard to find as he was indexed as 'Harry Davey Rule'.
Working from the Census I have the following for the children:-
Henry Davey Rule bp. 03 June 1836 s/o Henry Davey and Elizabeth Rule of Town, miner.
Mary Anne Rule bp. 23 Dec 1837 d/o Henry and Elizabeth Rule of Ramsgate, miner. (this one is a 'maybe')
I cannot help with baptisms for the later children just now as I only have information up until the end of 1837 for Camborne.
The father is :-
Henry Davis (Davies) Rule s/o Richard & Anne bp. 26 Dec 1812 Camborne.
Other children for Richard and Anne:-
Richard bp. 28 September 1800 Camborne
Richard bp. 27 Feb 1803 Camborne
Anne bp. 02 April 1804 Camborne
Anne bp. 30 January 1805 Camborne
Catherine bp. 07 November 1807 Camborne
Margaret bp. 27 Feb 1810 Camborne
John bp. 09 Dec 1815 Camborne
Marriages that might fit here:-
11 November 1799 - Richard Rule, miner m. Anne James at Camborne (wit:- William Hocking, Henry Stephens)
24 December 1802 - Richard Rule, miner m. Anne James at Camborne (wit:- Oliver Rule, Mary Ann Rule)
** Now there is a 'Cat Among The Pidgeons' if ever I saw one **
Do we have one Richard Rule marrying twice to girls who share the same name (Anne James)
Maybe the Camborne Burials might help:-
Richard s/o Richard and Anne Rule bu. Camborne 19 September 1802
Seems not as that is all I can find with reference to this family at Camborne.
I will try and deal with Stephen and Olivia in my next.