そうです is a way of saying 'yes, that is certain.'
For example, a discussion using the word might go like this:
4+3=7 ですか? (Is 4+3=7?)
はい、そうです。(Yes, that is certain.)
On the other hand, そうですか is, as the definition you provided, can be both I see; or is that so?
If you used it as 'I see':
椅子に引っかかって腕を折りました。(I tripped on a chair and broke my arm.)
そうですか。。。 (I see...)
If you used it as 'Is that so?':
4+3=8です。 (4+3 is 8.)
そうですか? (Is that so?)
そうですね is a more intimate version of そうです、 and usually used when you are talking to a person of higher rank. It can also be used to start a sentence like 'um,'
Used like 'yes, I agree':
社長: ロッククライミングは危ないと思います。(Boss: I think Rockclimbing is dangerous)
社員: そうですね。(Worker: Yes, I agree.)
Used like 'um':
あなたはどう思いますか? (What do you think?)
そうですね、良いと思います。(Um, I think it is good.)
いいです and いいですね is the same thing as before, the one with the ね is more intimate version, and usually used when you are talking to a person of higher rank.
I hope this helps.