How to manage which profile details can the seller manage?

By default, sellers can edit all the profile details. If you want to have few of the profile items to be non-editable then you can set those fields in Seller Non Editable Fields under the Settings > Seller Settings section in StoreHippo admin panel.

For details on seller settings, please refer to the following topic:
http://help.storehippo.com/topic/seller-settings