Since ConnectBot doesn't use any of the normal TextView widgets, Android's IME structure isn't designed to directly support it.
The best way to use Android with a virtual keyboard is in Portrait mode. By default, ConnectBot is set to use Portrait mode when no hardware keyboard is present. To change this setting, go to Preferences from the Host List.
In Landscape mode, the Android virtual keyboard (or other IMEs) will take up the entire screen. Android provides no way for ConnectBot to resize the terminal view in Landscape. However, you may use a work-around: Force Resize to fit above the virtual keyboard if desired.
On devices without a hardware keyboard, you may press and hold the MENU button to bring up the virtual keyboard. NOTE: This applies to any program on the Android platform; it is not ConnectBot specific.
You can enter any key combination with ConnectBot and the virtual keyboard, but you must know how keys are mapped on a normal console. For instance, usually combinations of ALT+letter on a PC keyboard are actually mapped to sending, sequentially, ESC key then the letter.
Note there are also screen gestures: see the ScreenGestures help topic. for Page Up and Page Down.