1) There are about 1300 photos in my wife's photo stream/iCloud library (those are the same thing basically,
No, My Photo stream and iCloud Photo Library are different features of iCloud.
- My Photo Stream is a buffer in iCloud for transferring photos between devices, it is not a permanent storage. Newly added photos will stay in My Photo Stream for a limited time to be downloaded. After a month they may be replaced automatically by newer photos. Use this only to transfer photos, not as a cloud storage.
- iCloud Photo Library is a central storage of your Photos Library, and all changes to this library will be updated across all devices that are using iCloud Photo Library. This library is meant to be used to store your photos in a central location.
How long will it take for the photos to "sync back" to the Photos library on my iMac? I tried doing this, and nothing happened for about 5 minutes...maybe I was just being impatient!
It will take much longer than you like. It is hard to estimate, but usually the download takes as long as the upload. It will depend on the size of your library and your network. For my library of 40000 photos it took three days using a wired Ethernet connection.
2) In order for this to work, I have to log my iMac into my wife's iCloud account in system preferences, correct?
My advice will only work, if it is indeed an iCloud Photo Library, and you should do it from an account, where your wife is signed in with her iCloud AppleID.