Yes you can sync “your” mailbox and calendar to your phone, if you want other people stuff to sync to your phone you will need to add their accounts separately to your phone. In the office on your pc though you can view whatever you want of staff as long as you have the appropriate permissions given to you on the Exchange server.
Out of Office etc can all be done using Exchange. Having Exchange also gives you OWA (outlook Web access) and OAW (Outlook anywhere) so you can either logon to OWA page from anywhere with the internet or setup OAW so that as long as you have Outlook on your machine as long as you have an internet connection you will receive mail wherever you are.
Be aware though to utilise all of this you will need a copy of Microsoft Outlook running on your pc.
Phones will all be able to connect without the need for any extra software.
To use SMTP via exchange you will need you web/domain host to create/point your MX record to your external IP address of the network your Exchange Server is sat in, If it’s in the office you are sat in then just go to http://www.whatsmyip.com and it shall give you your static IP address for your connection, also you will need a “static” external IP address not a dynamic (your ISP can help you help with this)