No one else can modify the owner's role. Storage for the group is drawn against their quota. Only the owner can delete the group or transfer ownership to another member.
fcheslack answered the question about privileges -- the three things listed are the three differences between admins and owners; there are no others.
what do you mean by "storage for the group is drawn against their quota"?
Attachment storage in groups is counted against the Zotero File Storage quota of the group owner, so if the group has >300MB (or all libraries of the owner have >300MB) they'll need a paid account for attachments to sync (metadata will continue to sync either way). Any storage (paid or unpaid) by other group members is both irrelevant and unaffected by groups they don't own.
Beyond that, might be helpful to describe a specific situation you're looking at rather than asking general questions where it's hard to tell what answer exactly you're looking for.
How can an owner transfer ownership of a group library? (I want to purchase storage for a current shared library, but I"m not the owner, so the owner wishes to transfer ownership to me.)
The group owner, and only the group owner, can initiate transfer ownership on the group settings page. You get to that by clicking manage profile from the list of groups you're in, for example
Upgrade Storage
Storage for the group is drawn against their quota.
Only the owner can delete the group or transfer ownership to another member.
Beyond that, might be helpful to describe a specific situation you're looking at rather than asking general questions where it's hard to tell what answer exactly you're looking for.