New iphone 4

Apps are sycned to your computer. They are just files. You can copy them off to other computer and put them in iTunes.

All 3rd party apps on your iPhone should be in your iTunes library on your computer. You will need to transfer your iTunes library from your iMac to your MacBook Pro along with authorizing your MBP with your iTunes account with iTunes.

http://support.apple.com/kb/HT1751

There is no i-Device limit for the number of iPods, iPhones, and iPads that can be synced with the same iTunes library and iTunes account on the same computer.

If you have Sync Apps selected under the Apps tab for your iPhone sync preferences with iTunes, all apps should be in your iTunes library on your computer. With this selected, after downloading an app with your iPhone, the app will be copied to your iTunes library automatically the first time you sync your iPhone with iTunes after doing so.

If you don't have this selected - all apps on your iPhone are not in your iTunes library on your iMac, with your iPhone connected to iTunes, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone. After confirming all apps on your iPhone are in your iTunes library, select Sync Apps under the Apps tab for your iPhone sync preferences with iTunes making sure all apps currently installed on your iPhone are selected below followed by selecting Apply.

My new iphone 4 has been having the alarm go off at 4am for the past three days, and I have no alarm set for that time. It has happened multiple times, I've restarted and resynced and restored my phone...nothing changes.