Q: plentiful と plenty はどう違いますか?
A: 'Plenty' is a pronoun/noun.
"She has plenty of apples, so you don't need to bring her more."
^ It's typically said in this format (as shown above): "plenty of..."

'Plentiful' is an adjective.
"At the apple farm, the apples are sweet and plentiful."
Here it works like a standard adjective, but this is really formal. So it is probably heard in historical fiction, or used in formal essays.
Q: plentiful と sizeable はどう違いますか?
A: Plentiful means there is a lot in a positive way - 'the stars were plentiful / he had plentiful good qualities'

whereas sizeable is a more neutral term - 'there was a sizeable difference in our skills'

plentiful is uncountable /too many to count, whereas sizeable implies that the object could be measurable. it is often used to describe a difference. for what it's worth, plentiful isn't often used in natural conversation, I think it's a more poetic word.
Q: plentiful と abundant と affluent と copious はどう違いますか?
A: Plentiful is not related to abandon.

Plentiful = many, lots of.
Abandon = to leave.

These words do not have a similar meaning.

Affluent = to have lots of (money, property, or materials)

Copious = large in quantity, many.

Copious and plentiful can be used in the same way. Affluent is often used when describing things related to wealth or rich people.