iPad Air 5th Gen issues with 18.0.1

Starting with your third item concerning Safari bookmarks...

Settings > Apps > Safari > Advanced > Website Data - use the Search dialogue to find data for "apple"

Identify the cdn-apple.com entry; with your finger, swipe the entry to the left to expose the associated red Delete button. Delete this entry (and just the entry) from the list.

Having deleted the entry, you can leave the settings page - and restart Safari.

As for your other difficulties, try a forced-restart - as this will often clear an isolated or post-update software issue:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

If the problem persists after performing the restart, it may be necessary to reset your iPad settings. While this reset will not cause any loss of data, as a precaution, it is always wise to ensure that you have a current iCloud or iTunes backup before performing the reset:

How to back up your iPhone, iPad, and iPod touch - Apple Support

When you are happy to proceed, you can perform the reset from iPad settings:

Settings > General > Transfer or Reset iPad > Reset > Reset All Settings

If the problem still doesn’t clear, the next step is to reset the iPad to factory settings:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Otherwise, you would be best advised to seek assistance directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively and perhaps easier, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to assist with troubleshooting:

Genius Bar Reservation and Apple Support Options - Apple

I misinterpreted your initial post concerning bookmarks - in that you might have been seeing duplicate bookmark icons. Given your screenshot above, this clearly isn't the case...

A change has been made with iPadOS 18.x - in that more bookmark icons are shown across the width of Safari's Start Page - the Start Page being seen when opening a new tab. This appears to be an intentional change in iPadOS 18.x Safari.

Bookmark icons are now shown across the near full width of the Safari App window (per your screenshot), whereas earlier versions of iPadOS only used the central area of the App window (leaving proportionally more empty white-space to either side). While you can reduce the number of visible rows shown (tap Show Less - reducing the visible icons to just two rows), you cannot otherwise alter the appearance.

Here is an example screenshot taken from my own iPad Pro running iPadOS 18.0.1: