How to connect my iPhone to PC and edit my contacts and other things like I can do with my Nokia phone?
You can in iTunes define which online Service or PC program you want to use.
In the iPhone User Guide on page 55, are the below written.
The Info pane lets you configure the sync settings for your contacts, calendars, email accounts, and web browser.
Sync contacts with applications such as Mac OS X Address Book, Yahoo! Address Book, and Google Contacts on a Mac, or with Yahoo! Address Book, Google Contacts, Windows Address Book (Outlook Express), Windows Contacts (Vista and Windows 7), or Microsoft Outlook 2003, 2007, or 2010 on a PC. (On a Mac, you can sync contacts with multiple applications. On a PC, you can sync contacts with one application at a time.)
If you sync with Yahoo! Address Book, you only need to click Configure to enter your new login information when you change your Yahoo! ID or password after you’ve set up syncing.
I use iCloud to sync the Contacts from my iPhone. I can then view and edit changes Contacts from the iCloud site on any PC.
FYI, an iPhone connected iTunes on a Mac can sync contacts with the Mac's Address Book.