Congrats on your now MacBook Pro and welcome to the Apple family!
So, I'm just going to address each question directly.
1) Short answer: yes. The article "iTunes 11 for Mac: Download previous purchases from the iTunes Store" goes over the process of downloading all of your previously purchased content.
2) When you plug in your device you should see that iTune will allow you to configure the syncing options for each type of content. See "iOS: How to transfer or sync content to your computer" for more info.
3) Automatic downloads is something that you can disable, but is enabled by default. This is also something that be different for Music and Apps. See "iTunes Store: How to enable Automatic Downloads"
It's a lot of information, but that should help you out and enjoy your new MacBook Pro!
griff, thanks for your answer that helps me!
I'm starting to think that it is not possible to prevent new purchases made with the iPhone to be downloaded to the Mac as soon as I open iTunes (ref. my question number 1). It is definitely important to be able to tune the iTunes to prevent automatic apps downloaded as you have correctly reported with answer to my question number 3.