Yes, you can vote on the challenge that you submitted. Challenging a Newsroom and voting for a challenge are two distinct actions. Each action uses Civil tokens from different accounts. When submitting a challenge deposit, you use Civil tokens from your Available Balance, while you'd use Civil tokens in your Voting Balance to vote.
The Civil token deposit for a challenge is locked in the rewards pool (like an escrow account) that is distributed after majority/minority votes have been decided. You can use voting tokens to vote in as many challenges as you want – including your own. This is similar to an election, where candidates may vote for themselves.