Isn't it possible to backup iphone text messages (including photos inside) with Cloud? I'd like to print out the messages but I first need to get them to display on my computer so my idea is to log in to icloud via firefox and print from there. All I can find is iCloud > Backup & Restore which looks like a general backup.
There is a difference between icloud backup & restore and icloud sync. "Backup and restore" simply backs up your iphone data (including sms text messages and photos). This data can only be used to restore an iDevice (such as the same or another iphone to factory settings).
iCloud sync, on the other hand, pushes your iphone contacts, notes, reminders, emails, calendars to your iCloud account.You can indeed log in to iCloud to see this data. SMS messages are not included in data related to iCloud sync.
So, to answer your question - no, you cannot log in to icloud and print out the iphone text messages from your PC. You can, however, backup iphone messages along with photos and display them on your computer using third party tools: How to backup iPhone SMS text messages?