1/ is easily checked yourself
Pulloxhill baptisms and marriages have been extracted onto the IGI. You can access them via the Hugh Wallis site at
http://freepages.genealogy.rootsweb.ancestry.com/~hughwallis/IGIBatchNumbers/CountryEngland.htm#PageTitle which cuts out all the extraneous member submissions and enables you to just look at Pulloxhill extracted entries. You'll find the detail about Lyddy and Ellen's parents which you requested.
2/ There are no Hallsworth marriages in Pulloxhill, but there are two Hallworth marriages, nor is there a marriage in Beds of Margaret Hyde
(and bear in mind that just about all of Beds marriages pre 1813 have been extracted onto the IGI*). What other details are on the licence other than what can be found on Shotley taxpayers on Ancestry??
3/ What's the evidence that the Hallsworths were born in Pulloxhill? There are no Hallsworth baptisms in Pulloxhill before 1773, but there are earlier ones in Higham Gobion (see next para).
The first Hall(s)worth burials in Beds were in Nov 1777 with Ann and William in Pulloxhill. Might these have been the parents? Might also have been Ann and William, children of Thomas baptised in Higham Gobion in 1773 and 1771. You'd need to consult the transcript to see if there's any extra information. It looks as though James may have moved first to Pulloxhill with Thomas following a year or so later, judging by the baptisms of their children.
David
* Looking at Hugh Wallis it seems that Higham Gobion marriages are the exception! Nor are they on the BVRI. Very strange
That probably is where the marriage took place, particularly as James and Margaret were both of Higham Gobion on the licence (as was Thomas who presumably was the bondsman)
Late edit! The VCH entry for Higham Gobion says "The registers are incomplete, the first book going from 1585 to 1727, and the second beginning in 1785." See also http://www.nationalarchives.gov.uk/a2a/records.aspx?cat=004-p125&cid=-1#-1 which shows that there are no BTs for 1772 either. Looks as though you're out of luck.