Which email addresses you mean? Do you mean collected addresses or your contacts’ addresses?
I’m referring to my address book as listed in my Outlook address book. Also how can I sinc my calendar with my Android phone?
In that case simply use Search bar in the Contacts area - you should be able to search all your contacts easily.
As regards the calendar, set the calendar account in both eM Client and your Android phone and the synchronization should start automatically.
how do I set the eM client calendar account?
eM Client does not support Outlook.com calendars yet but you can expect it in the upcoming version 6. In the current version you can set all CalDAV using Calendars and Google Calendar of course.