Hello,
1 &3 are very broad questions: I suggest taking a look at
http://www.apple.com/support/itunes/getstarted/
iTunes 11 tips: the complete guide to iTunes on OS X | News ...
iTunes User Guide: How to Use iTunes - iSkysoft
2) Almost all songs are priced, but sometimes Apple offers random songs for free (ie 'Free Song of the Day'). This does not prevent you from importing CDs into your iTunes library, or adding any other mp3/AAC audio files you have.
4) iTunes doesn't natively support this feature. iTunes only supports syncing to iOS devices. Depending on your phones' OS, there may be third party software available to enable syncing compatibility. For example, I know Android devices provide software for syncing music to your phone (though not directly through iTunes, AFAIK).