Where's the search history button?
In Chrome's interface the search history has been integrated into the back button – just hold down the mouse button when you're clicking on the back arrow. After a short delay, a menu pops up showing your recently visited pages. You can also access the full (searchable) history from that menu.
Where's the home button? Where's the favorites bar?
By default Chrome has no home button. You can enable it by opening the options dialog – click the wrench icon in the top right and then "Options" – and checking the box labeled "Show Home button...".
As for the bookmarks bar, whether it shows for you by default depends on your previous browser settings. To show it or hide it, hit Ctrl+B.
Does Chrome work together especially well with Google services like Gmail, Google Maps, or Google Docs?
Additionally, Chrome ships with the Google Gears plug-in, which is used in some Google (and some non-Google) apps to deliver offline functionality for web pages and more. But don't expect Chrome to work much better, or even work at all, in all of Google services.