Question about multiple entries

Am I allowed to submit both a personal and a team entry?

If so, is this following scenario possible?

I enter both a personal and a team entry. The team entry does not win any prize, but my personal entry wins first place. As I am “part of a registered VRC, VEX U or VEX IQ Challenge team”, the team I am on qualifies for worlds.

No, this would not be possible within the same online challenge. For each challenge, only one entry per team is allowed. Because your team number will be on both your individual entry AND your team entry, this would be considered a double entry, and is not permitted.

Good luck!