There isn’t anything different about the creator program payouts from typical partner commissions. Task payouts will appear as pending actions according to the immediate locking and clearing schedule defined in the contract.
No, you aren't required to use tracking links. impact.com gets social insights per post like shares, likes, engagements, comments, etc. without using links. You'll need to use links or promo codes to track performance. It is possible to track performance even if there is no associated payout for the campaign. So, if you're doing flat fees only you could still use links to track performance.
Performance by Campaign Report 
Yes, a template term is always required to create a relationship with creators regardless of the campaign compensation type.
For a creator to be paid, they must have a contract with you by joining your program’s template terms. These terms specify payment timelines and other business terms.
When a partner starts working on a specific campaign, they will accept your SOW (Statement of Work) for that campaign. The SOW will indicate the deliverables they will produce, such as the type of content, the platform on which they post, and their compensation. Once a campaign is over, the Creator will remain a part of your program (unless you remove them).