What will be removed if I sync my device with another iTunes? I had to blow my old iTunes installation. I have all my music and a up to date backup, but I still want to sync my device to change some content. iTunes warns me that "the content of the iPhone will be deleted". What is "content" here? Does it include contacts, messages, apps? Or is just music, books and pictures?
The answer depends on how your phone is configured for synchronization.  Note: If you back up your content from the phone to the local new computer first, then though some data will be erased, it will then be copied right back on to your device.

Entertainment files:
In most all situations, your music, movies, podcasts, books, and TV shows will be lost as they are replaced with information from the new computer. Apps will usually be preserved.

Contacts and calendars:
If your contacts and calendars are being synched through a cloud service, like most people today, your contacts and calendar data won't be lost. If your contact and calendar data is being synched locally through the computer directly, then yes, it would be lost and replaced with the new local data.