Images that load from other sites stay hidden in a Mail message until you choose Show images for that message, or Always show images from its sender. Loading them lets the sender see that the message was opened, so each person decides for themselves, including in a shared mailbox. Images attached to a message are now shown in it.
While Inbox is open, new mail appears in the list within about 15 seconds, with a message saying how many arrived. It checks less often when the page has not been used for a while, and not while the tab is hidden.