No for Jira Cloud
For Jira Server and Data Center, you can extend 5 times

Server and Data Center can only be purchased yearly.

Not exactly pay per user. According to Atlassian policy, you pay the pricing tier you fall into. Example for the server version if you have 25 users you pay the pricing tier for 25 users (11-25 users). But add one more user, which makes your total 26, and you pay the pricing tier for 50 users (26-50 users).

Data Center apps are sold as an annual subscription. You are eligible for support and version updates as long as your subscription is active.

If app pricing changes after your initial purchase, there’s a 60-day grandfathering period during which you can renew based on the old pricing.