How does this database design look?
Your design doesn't record "which user submitted which answers".

Should there not be a relationship between SUBMISSION and USER?  You have the attribute submission_user but you haven't indicated that it is a foreign key to USER.

Should there not be a link between SUBMISSION_ANSWER and ANSWER?  How else do you know which question is being answered and what the value of the answer is?

SUBMISSION_ANSWER.attribute_name seems like you left something incomplete.