First off welcome to the forums
1.) Through the use of iSyncr
you can flawlessly sync your iTunes music to your Android device over Wifi or USB connection.
2.) I use an app called Unified Remote
and it controls music on my computer over Wifi pretty nicely and i am sure it could work for you too
3.) Well you can use them if you please, download them if you want, there are Widgets that basically are live feeds that you can place on your homescreen or any screen to show you quick updates
4.) I know AT&T offers this feature so you can go with them if you want it. Otherwise i know Verizon does with this app: Visual Voice Mail
, about the only good app Verizon has. Otherwise Google Voice has a pretty good voicemail system you could look into
5.) Definitely integrates great into Android
6.) The default email app lets you set up IMAP or POP accounts
7.) I know there a numerous apps for Browsers that create a great experience like Dolphin HD
There are a lot of good smartphones out there right now. Most notably the Nexus 4 (Only on GSM Carriers, AT&T, T-Mobile), Galaxy Note 2, Galaxy S3, Droid DNA, etc
Plenty of phones you can look up and check out.
Battery life is kind of a concern then you might want to get a device with a removable battery, Samsung has typically always had devices with Removable batteries, while HTC is kind of leaning towards non-removable...
The Nexus 4 and Droid DNA are non-removable, while the Note 2 and SGS3 are both removable!
Hopefully you find some of this information useful