Partial answer (first part) -
--Edited in an attempt to further clarify my thought process--
Each line has two parts: a word and a clue. We're grabbing the common characters between the two
Tomato and the mouse’s nemesis
Tomato
"the mouses's nemesis" - Jerry (the antagonistic mouse) considers Tom (the cat) his nemesis
The shared characters are TOM
Nor is it a connecting option that
Nor
"a connecting option" - or is a conjunction that has common letters with 'Nor'
The shared characters are OR
Crows go gently down the stream.
Crows
"gently down the stream" - I think of row, row, rowing a boat
The shared characters are ROW
Answer:
Put them all together and you get TOMORROW
Tomorrow is the next day and therefore begins the future
'Tomorrow' never actually comes, it is always 'Today'