Can two spouses share an Apple ID?

You can, but you will eventually (if not sooner) run into many problems such as getting each others email, messages, photos, etc. Everyone should have their own unique Apple ID. If there is information you want to share with your spouse, use Family Sharing instead. Then you can control exactly what you want (and don't want) to share with your spouse.,

Set up Family Sharing - Apple Support

Yes. Both parties will affect synchronization between two devices using the same AppleID and iCloud.