"Since Godel's Second Incompleteness Theorem says we cannot be sure the system is consistent, is there a way to know for sure whether any given statement is true AND there does not exist any proof in that system showing the statement is false?"
As talked about in the comments, I will assume we're talking about the appropriate formal mathematical systems.
Well, it depends on what you mean by 'know for sure'. If you mean being provable from within the system, the answer is no we can't be sure. Leave off the first part about being true... we cannot even prove that "there does not exist any proof that within a system that a statement is false".
The thing to note is that if one contradiction is true within the system, then every contradiction is true, by the principle of explosion:
So "a contradiction exists in the system" implies "all statements are provable in the system".
The contrapositive is, "not all statements are provable in the system" implies "there does not exist a contradiction in the system"
So if we were able to prove that any given statement is not provable within a system, we prove that there does not exist a contradiction within the system. But that would prove the consistency of the system. Which violates godel's 2nd incompleteness theorem.
So a proof from within a system that a given statement is not provable within the system would violate godel's 2nd incompleteness theorem.