Apple connectivity with Android devices
First, I am an pure Android user. I have never owned an MAC, so I can't comment on everything.


Since both use iCal, some kind of sync should be possible. But I wouldn't recommend that.
IMAP is no problem and you lose nothing. IMAP is supported by Android's mail client and K-9.
You don't need GMail for contact sync. I would recommend using Google contacts.
Android's philosophy is much about cloud backup and restore, therefore it's a feature of Android. But since Google can't fore the Apps to use that or even force the manufactures to enable the BackupAgent it's not 100% available for non-Google Apps/Devices. But if you have root and TitaniumBackup, the device can easily be saved and restored completely.
No problem at all here. It should work with any modern Android device.
Can't comment on that


I think that if you buy an Android device you should also use the Google services (besides GMail in you case, but that's no problem. I also don't use GMail, but everything else). So for 1. 3. and 6 that is Google Calendar, Google Contacts, Google Docs (now Google Drive, good for notes) and Google ToDo. If you ok with having your data within the Google cloud. But the synchronization is just awesome. You can use every Google service with the Google WebApps (or Chrome Apps) from you MAC

Other solutions are most likely some 3rd party tools that try to build a bridge from the Google world to Apple. Which may or may not work, may needs to be purchased, etc. There are just to many pitfalls that impair the experience.