I have no good answer for 'next night', but I commend to you 'yestreen' -- a word meaning 'yesterday's evening', which was still in (possibly affected) use in the 19th century. That may be Scottish; a more English version is 'yester-even'. See also 'forenight'. The first use of 'yestreen' noted in the OED was 1400 -- not necessarily Old English, but definitely unlike modern English.
Also, you may be pleased to know the existence of 'Saturnight', 'Sunnight', 'Tuesnight', 'Wednesnight', 'Thurseven' and 'Frinight'. In all cases, these referred to the night before the corresponding day. They are all labelled Old English -- so, earlier than 1400.
It might not copy perfectly, but here is the OED's earliest noted use of 'Thurseven':
Prose Charm: Against Elf-Sickness (Royal 12 D.xvii) in G. Storms Anglo-Saxon Magic (1948) 222 Gang on þunres æfen, þonne sunne on setle sie, þær þu wite elenan standan.
I can't help you with a translation.
A pleasing word meaning 'the end of the night, just before daybreak' is 'ughten', but the etymology isn't clear to me. It's in Beowulf (~1000AD) and fitted into the Germanic/Saxon/Old-English mishmash at the time.
Straying into invention, I suggest 'to-fall' -- a word meaning 'beginning of night', whose examples in the Oxford English Dictionary (which I've used for all the words listed) all look to the future. It was first used in 1425, though not in the meaning we're discussing.
Yes, "looking suspicious" suggests that something about the group's appearance merits suspicion. One of these options might better convey your meaning:
The group was standing at the corner, looking on suspiciously.
You could also use "watching suspiciously," or rephrase this way:
The group watched suspiciously as [the activity transpired].
Best Answer
Cambridge dictionary defines overhear as
(link)
Oxford dictionary defines the word as
(link)
Lots of times you "overhear" someone by accident and then it's your choice whether to keep listening intentionally or not to do so. When you begin to intentionally listen you are not really "overhearing" someone or something, rather you're deliberately listening to someone, probably without their knowledge–and that becomes eavesdropping.
You've shown that the American Heritage dictionary does not mention anything about the hearer's intentions but the two dictionaries I cite do so, with Cambridge including the 'accidental part" in the meaning. Two or three other dictionaries–including the Oxford English Dictionary, Merriam-Webster, Collins–do not mention the hearer's intention, but this is not as full a definition as the two I've included, and with which other speakers agree in comments.