If you look at your menu items, they have a property
ShortcutKeys[
^] which will (predictably) set the keyboard shortcut...
As for the Enter key, please don't.
This is a major change to the expected behaviour of the Enter key - that it is "I've finished - take this dialog away" which can only confuse users. It is strongly recommended that you do not change normal expected behaviour for one app - it confuses and annoys users and will normally make users more reluctant to use your application.