Can other users see how I use Gmail (e.g. when I read their messages, mark their messages as “not important,” mute a conversation, use labels and filters, etc.)?
No, how you use Gmail is your own business. Personalization features like Priority inbox, Smart Labels and custom filters enable you to tailor Gmail to your needs. The way you use Gmail’s customizations and the way you handle your mail (e.g. whether you mark messages from someone as “unimportant” or set a filter to archive them) are not visible to other users.