The first extract is not an allegation but a bond -- a promise to make a payment if certain conditions are not met. The conditions are normally set out in the second paragraph (in English, below the Latin).
Joseph Painter was acting as 'bondsman', in support of Richard Mousely. He may have been a relative, but not necessarily – a bondsman might be a close friend, business associate, etc., and bonds don't normally state relationships. His chief role in this context was to support the groom in paying the penalty, in the unlikely event that there should turn out to be a legal impediment to the marriage.
Your second extract is simply an instruction for a licence to be granted so that the minister can marry them. You will need to look elsewhere for a record of the marriage itself ...
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Let a licence be given to the minister of Mancetter for a marriage between Richard Mously of Atherston in the county of Warwick, chandler, aged 22, and Jane Towe of Chilvers Coton in the aforesaid county, spinster, aged 21. The aforesaid Richard Mously and Joseph Painter of Nuneaton, tailor, were bound.
Richard Mously was sworn before me, John Foxcroft, surrogate.