The Renew button does not appear on the Membership tab for a contact

The Renew button only appears if the membership level renewal period is set to something other than Never, and if there is a specific renewal due date in the member record. The button will not appear for members with recurring payments.

The recurring payments option does not appear on the Renewal policy tab

Recurring payments are only supported for Community plans and above, and not for renewal periods greater than 1 year.

I suspend a member but his recurring payments still take place

If the member has recurring payments with PayPal, suspending the member will not stop the recurring payments on the former member's card. The recurring payments must be stopped manually.