How can we autocreate an organic group during registration How can I do this using the rules module?:
User registers (as profile type a) -> create organic group using field value from registration and make the user the manager/admin of the group

I have also the modules Profile 2 and Profile2 Registration Path.
Creating a group is really just creating a node.

Create a rule that reacts on "After saving a new user account".
Add Action: Create a new entity. 

Set content type to: Group.

You can set the title of the node (the name of the group) to the new user's name or any value you want using available tokens.

Set the author of the node to the new user (it's usually called "account" in rules) and the new user will be the owner/manager of the group.