Paying it off won't boost your credit score as much as keeping the available balance below 50% of your available credit limit. Credit cards are extremely powerful in boosting credit scores if managed properly
You can't purchase a credit score. You build a credit score by honouring monthly payments to your creditors. If you don't have any active accounts open a small clothing account and pay the account monthly. You will in no time generate a credit score for free
There is no clear answer on how credit scores gets calculated. Each bureau has it's own distinct formula they work with. I have come across this good article explaining the different credit bureau score cards https://creditsalvage.co.za/index.php/all-blogs/41-ultimate-credit-score-guide-2020