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I am a volunteer for the Oxfordshire Family History Society and have spent a little while scrutinising the Benson parish records from 1560 (when they began) to 1612 for Costar (and variants: Chostard, Costarde, Coastard, Chostard, Coster, Costerd(e), Costord, Coustard, and Costerr)

I am afraid I cannot find either a baptism or marriage in Benson for Thomas Coster.  The very first mention of the name appears in the baptism register:
12 May 1594 Edward, son of Thomas Coster followed shortly afterwards by
6 Jan 1595 Jean, daughter of Thomas Costerr

The only Coster marriage I can find is
1 Oct 1598 Thomas Nash married Florence Coster

And a search for burials brought up
17 Jun 1591 Susan Costerde, wyf
1 Apr 1618 Thomas Coster, senex
18 July 1635 Widdowe Costerd

There are however quite a lot of records of Costars in nearby parishes, e.g. Cholsey, For example, there is a Thomas Costard baptised in Cholsey in 1568

Nowhere in Oxfordshire can I find a Thomas Costar (or variants) marrying a Katherine so I would ignore that "hint" from other trees. 

I hope that this is helpful information.  Do respond if you would like any further research done by the Oxfordshire Family History Society

OFHS volunteers Alex and I have researched William Dearing/Deering son of Richard Dearing in Steventon for you.  We have found a baptism on 16 Sept 1596 on Family Search and the Berkshire baptisms on Find My Past

We have noted the baptism on the OFHS AB03 transcript and believe that this was erroneously transcribed as 21 Sept 1596

We have noted on the transcript the burial for William Deering on 18 Sept 1596 but we have been unable to find this on either Family Search or Find My Past

On visiting the OHC search room to check with the Steventon microfilm, film number 146, we find that this is the only one which is "currently unavailable".  No doubt it will be returned in due course, so we will look again next time we are on duty, i.e.  14 November.

Best wishes
Elizabeth and Alex
OFHS volunteers