Hi Fabottm,
For help with adding a website icon from your Home screen, the steps below found in the guide here can assist. Bookmark a website in Safari on iPhone
"Add a website icon to your Home Screen
You can add a website icon to your iPhone Home Screen for quick access.
On the website, tap
scroll down the list of options, then tap Add to Home Screen.
Note: The icon appears only on the device where you add it."
When removing the bookmark you should see three options:
- Delete Bookmark
- Share Bookmark
- Edit Home Screen
As you're not seeing the option, check your iPhone restrictions to ensure you can make changes to apps and your Home Screen. The article here can help you check: Use parental controls on your child's iPhone, iPad, and iPod touch The section "Prevent iTunes & App Store purchases" has a visual to help you ensure 'Deleting Apps' is enabled.
If you settings are correct, test removing the bookmark entirely using the steps in the guide page shared above.
Cheers.