The more natural sounding one or at least, the one I hear the most is "I wasn't impressed by it". "Impressed with it" allows for an odd structure which gives way to another definition for impression, to seal; to imprint.
As for your second question, a lot of people use either or expressions very loosely. To be "impressed" is to evoke admiration out of others.
I somewhat oppose certain adverbs modifying verbs/adjectives such as "very bad", "really good". Some of these words do quite well on their own. Bad is bad, there isn't any "less bad" nor is there a "less good" concept, I think.
Regarding your word however, one can be slightly impressed.
"I wasn't too impressed" can be used as a declarative statement.
"I wasn't that impressed" can be used to enforce your statement, making it absolutely clear- Hey, I think it was entertaining but I wasn't that impressed by it.