Abbreviated Dialing means to dial a specified number (speed dial) to reach a predefined assigned destination. You add abbreviated dials via ccmuser page for example and invoke it via the AbbDial sofkey, then enter the assigned number to trigger the speed dial.
This is well described in CUCM SRND, in a nutshell Globalization means that you format the number into a full +e164 form, such as +12125551234 for US numbers for example as calls arrive to the system, as well as your normalize the dialed numbers as they are dialed.
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...