ter summat stronger if yeh've got it is used to show heavy accent or a dialect by writing words as they are pronounced (see Phonemic orthography). Here ter would be the phonemic orthography of to: I wouldn't say no to something stronger if you 've got it, mind. (I have written in bold the words that were replaced to imitate accent.) This site indicates that this is how to is spelled in Eye ...
0 There is also a usage trend to use - tor when the intent is to emphasize that the agent is a person, while - ter is used when the agent is not necessarily a person. For example, ‘compu tor ’ the original term meaning a person performing computation later becoming ‘compu ter ’ when calculations were performed by either people or machines.
When is the suffix -tor and -ter used? - English Language Learners ...
A clue to Hagrid’s regional background may come from the rhotocity implied by the post-vocalic ‘r’ in syllables where in the standard pronunciation variant the schwa should be present: ter, inter, tergether, etc. This rhotocity survived only in areas west of London, south of Birmingham and in Lancashire.
There being basically means something like "because there is". #1 and #3 sound good to me, because there is an exam tomorrow and there is a dispute, but #2 sounds wrong to me, because there isn't a murder right now, the murder is something that already happened. I would phrase it as "There having been a mysterious murder", because there has been a murder, not there is a murder.