The missing lines at the bottom is a bug that got fixed just after this release. The next Secure Shell release won't have the issue.
And your browser size issue goes away if you open the terminal in its own window. Chrome even has an "Open as Window" option (right click on the Secure Shell icon) to open in a window with no browser UI.
You can file bugs on the chromiom-os project.
Additionally, it doesn't even work right. In a screen-controlling app like vim it seems fine, but in the normal shell, once I enter enough text to use more than a screen, the bottom-most line is actually off the window (even if I scroll down).