Can I remove texts and photos from my iPad without it affecting those on my iPhone

Yes - if you disable Photos in iCloud and Messages in iCloud respectively:

For iOS/iPadOS16:

Settings > [Your Name / AppleID] > iCloud > [Apps Using iCloud] Show All

• Photos > Sync this iPad - set to OFF
• Messages > Sync this iPad - set to OFF

For iOS/iPadOS15 and earlier:

Settings > [Your Name / AppleID] > iCloud >

• Photos > iCloud Photos - set to OFF
• Messages - set to OFF