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'

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 connective option that

Nor
"a connective 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'

Partial answer (first part) -

Tomato and the mouse’s nemesis

Tomato and Tom (the) cat = Tom

Nor is it a connecting option that

Nor and or = Or

Crows go gently down the stream.

Crows and row = Row

Answer:

TOMORROW is the beginning of a new future, and is perpetually yet to come

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'