need need

Assuming this is a title, I would use "Needs".

oOld people need to be cared for/taken care of when they are ill. p Plants need to be watered. Old people need to be cared for/taken care of when they are ill. Plants need to be watered.

old people need to be cared for when they are ill. and plants need to be watered. old people need to be cared for when they are ill and plants need to be watered.

oOld people need to be taken cared of when they are ill. p Plants need to be watered / must be watered regularly. Old people need to be taken care of when they are ill. Plants need to be watered / must be watered regularly.

You could also combine this into one sentence as follows if you're trying to compare the two situations or show how they are alike: "Old people need to be taken care when they are ill and plants must be watered." or "Just like old people need to be taken care of when they are ill, plants must be watered regularly."

or: oOld people need caring/care. Old people need care.

"Old people need care." seems more natural or correct.

which one is correct? which one is correct?

Both are fine, both sets of sentences express the same idea or thought anyway.