Who is allowed to invite people to a Minecraft Realm?

I'm considering buying a subscription to Minecraft Realms (on PC) as a gift for somebody I know. Mojang doesn't have a gift option, and I don't want to spoil the surprise, so I was thinking I'd just buy it myself and give them access.

If I do this, will the recipient be able to turn around and invite their own friends? Can I grant them "admin" access to the server?

No, only the person who paid for the Realm can add people (source: am op on realms) I would recommend printing out a picture like this:

_{(source: minecraft.net)}

Write on the piece of paper, explaining that you are paying for a Realms subscription. Fold the paper up, and wrap it in a box.

What you could do instead is go to EB games, or GameStop and buy a minecraft realms subscription card and give that to him.