Can I claim a piece of someone else’s prize if I give them the idea (in the open entry) that propels their project into a winning category?
Only if you are a co-applicant. Otherwise, if you comment on an entry, you are doing so freely and voluntarily with the knowledge that you are not creating any ownership rights for yourself. It is theoretically possible for a technology expert with a good entry to meet up through the comment process with a community expert and want to invite them to join in as a partner in a revised entry. But that’s up to the original applicant.