Redpen supports Chrome browser extension, and it is free to use.
Yes, you can use Redpen for free with limited features.
No, you will have to purchase a new subscription for each Jira site you want to use with Redpen.
No. Atlassian bill organizations on a monthly pay-as-you-go. So when a new monthly billing cycle is triggered, you will be charged for the whole month. The subscription will be valid for the monthly billing cycle for which you have already paid even if you have canceled the subscription mid-month.