Thank you horselydown86, JenB and Bookbox for these replies - very quick and very helpful.
Initially, I didn't say what I thought because I did not want to colour anyone's interpretations, but I have looked at every entry in those 82 images comparing words.
a) Yes, I also felt that Gul. Hedley was William Hedley, but to me the matrina in the Donkerley baptism looks more like Marg:. The Hedleys stood sponsors for several baptisms and one of the other priests had much more legible handwriting.
I've looked around and there was a Catholic William Hedley married to a Margaret in that area in that time frame.
Please will you look again at that for me?
b) On the second line between fils: and Donkerley, there is one hard to read character. Is it really an ampersand? I took it to be the initial of the forename of the father, but I can't decide what it is. From what I know of this family, there are several possibilities for the father's forename, but once again I don't want to colour anyone else's views by saying.
Yes, I suspected that Prot. means Protestant. The word is completely spelled out in some of the other entries. But I cannot figure out the last word on that second line. It looks like nafzotmy which is gibberish to me.
Please will you look again at that word for me?
c) That register was quite a hodgepodge of items - baptisms, marriages, deaths, lists of communicants, a domestic housekeeping account for a cistern and what appear to be reminder notes from the priest to himself. One of those notes mentions Donkerley, which was a very commonly-found surname in Lancashire, and there were small clusters in Yorkshire, but it was quite rare in Durham and Northumberland so I have to consider it significant.
May I please impose one more image on you of that note? It is image #58 of 82 in that register.
Gratefully,
Westoe