As I understand there is no official software to work with HTC phone on the mac. So how can I manage my phone contacts, create backups of my phone and so on?
A few links for you (unfortunately, there aren't any free options out there)
The Missing Sync ($29.95)
By Mark/Space, this software allows you to do just what you described to manage your phone contacts (with Address Book), calendars, text messages, music, video, notes, etc.
But as far as their website goes, they don't support backups.
My Backup Pro ($4.99)
My Backup Pro is not a Mac application; it can be found on Google Play. Quite simply, it is backup software that allows you to backup online or to your local SD Card. Note that it looks like they have a free version for rooted devices.
Note that you can always try doing the tasks these paid applications do yourself by connecting your phone as a filesystem to Mac: