My wife and I have separate Apple IDs. In that case, will we be able to both have access to the whole library and make additions/edits that sync across all devices?
The iCloud Photo Library is tied to the AppleID. If you want to share one iCloud Photo Library on all your devices, you would have to use the same AppleID. That would be inconvenient, if you want to keep the email and contacts and other files and documents private.
You could both have your iCloud Photo Library (and thus pay twice for the cloud storage) and import each others photos into your private library.
Can we share selected photos/albums with other people so that they could view the photos but not edit the library?
See the link zinacef posted: - iCloud Photo Sharing - Apple Support
iCloud Photo Sharing lets you share selected albums, it does not require a paid iCloud subscription. There are just limits to the number of albums you can share, to the number of photos in an album, the upload rate.
See: iCloud: My Photo Stream and iCloud Photo Sharing limits
But it Shared albums are quite simple to use: Create the album, invite subscribers, then add the photos you want to share to the album. Whenever you have a new photo you want to share, add it to the album. It is essentially a stream of shared photos.
If the answer to the above question is "yes," do those other people need to view the photos on an Apple device, or could they view them in a web browser?
You can publish shared albums as a public webpage. This page will not really be public, you have to send the URL to the subscribers, who do not have an Apple device. They can then view the shared photos on a web page and download them .
