Mac – Time Machine restore on new OS

1. Yes - if you haven't excluded the /Applications folder from the Time Machine backups.

   As for system patches - you're installing a new OS. Once you finish, load up the Software Update and it'll pull down the most recent Combo Update for you. Actually, it's better to use the combo update than a collection of patches you would have otherwise.

   For more on this go to System Preferences → Time Machine → Options. It'll tell you what, if anything, you've excluded.

2. No. As long as you have sufficient space, you'll be fine. It doesn't need to be an identical drive.

In the Applications directory, there is a subdirectory called Utilities. In Utilities you'll find Migration Assistant. Or just use spotlight to launch it.

Migration Assistant has the option to restore from another machine, a Time Machine Backup, or another disk.

Make sure the TM disk is plugged in to your wife's new machine, and you should be able to select it from a list of volumes.