1) some parts are used by the OS itself and will not be listed. dont worry, its not missing or anything, just not shown.
2) yes this is the default behaviour unless the app specifies it or unless you root and do some modifications to force it to go to SD all the time during new app installs. Why the size of the app is reduced so much is because most of it goes to the SD card. a 20mb game may take up to 1-2 MB of internal space and the rest is stored on the SD card. The pros of this is increased internal storage space for apps (which is required to install apps, no internal storage = cant install any apps). The cons is that application load times *may* be longer although not noticeable and also during bootup, your application icons will take a wihle to load if you have a lot of applications in the SD because the OS will load these icons from the SD. This is completely normal,  you just need to wait a while longer and then your app icon should show up either in your homescreen (if you have a shortcut there) or in your app drawer.

hope this info helps.

for widgets you should not move them to the SD because the android OS seems to load up widgets only from the internal phone memory for some reasons, so if you want to use the application widget you'd have to bear the heavy space requirements that the app has.