Once you get to these dates in the 1600s, parish registers become patchy, and, as you have found out, usually only give a minimum of information. More often than not there are no wives names, no occupations for the grooms, no ages for burials etc.
The baptism of Richard in 1647 at Harberton just says father Nicholas.
Also at Harburton Anne 12 April 1646, and Nicholas 1 Feb 1644, also both just father Nicholas.
Then in Plymouth, Joane was baptised 19 Feb 1645, father Nicholas and mother Agnes.
Also at Plymouth Margarett 2 Aug 1650, again just father Nicholas.
There is also William 16 March 1646 at Plymouth, father Nicholas, mother Elizabeth.
How can you be sure Richard's parents were Nicholas and Agnes?
(Having said that, it's not beyond the realms of possibility the priest at Plymouth got the wrong mother's name for William, and she wasn't Elizabeth at all. It does happen)
I can't see any other baptisms to Nicholas and Elizabeth.
Normally the most useful route to try and sort out relationships is to find wills for the people you're interested in.
Unfortunately, most of the Devon wills were destroyed in the bombing of Exeter in WII.
I can't see any Emmet entries on the indexes on findmypast anyway, so it looks as if there were no wills for these people.