Are subscriptions extended automatically?

No, any purchase you make will not be automatically extended so you don't need to worry about missing a deadline for automatic renewal. After the end of your 3 or 12-month subscription, you can decide if you would like to pay for an extension. If you don't want to extend your subscription right away, you can extend it at the time of your choice in the future.

Incidentally, your purchases are always cumulative, for example, if you pay for 3 months now and after a month you decide that you really want 12 month's of unlimited access, then you'll have a full 15 months available. The paid subscription is valid for all of your devices, regardless which of them you used for the purchase.