Hi there, Pastel
In your firsrt sentence, "funny" would be an object complement.
In your second sentence, "that" can be ommitted, that's correct. But I'm not sure what you meant by the rest of your comment. If you meant that the whole construction "(that) it's funny" is the object of "think", you're right. But if you meant that "that" is an object and thus it can be ommitted, then you're not so right because "that" is only a subordinator that has no syntactic function within the clause.
Both sentences are correct.
Miriam