As the 'homeowner' (or any member who has the "Delete messages" permission), you can delete any message or post that's sent in your home.
On web: To delete a message/post, hover over the message and select the "Delete" icon
On mobile: To delete a message/post, hold down on the message/post and select "Delete"
Note: After deleting a message/post, it's probably a good idea to DM the person who wrote it to let them know that you've removed the content, with a short explanation why.
As the homeowner, you can remove and/or ban people from your home at any time. When you remove someone, they can rejoin (or request to rejoin) your home. When you ban someone, they won't be able to rejoin (or request to rejoin) unless you unban them. Because Geneva accounts are tied to people's real phone number, bans can be enforced at the most fundamental level (it's not like someone can just go create a new email address / account and come back and cause more trouble). Here's how to ban a member of your home:
Tap or click the member's profile (within in a room, or from the Member list)
Select "Ban member from this home" to ban them permanently or "Remove member from this home" (if you select remove instead of ban, they are able to re-join the home if they have the invite link). On Web, once you've clicked a member's profile, click the "..." menu and then click "Remove from home" or "Ban from home"