Can I restore Safari App after I accidentally deleted it rather than take off Home Screen? And is there an update to Safari because many websites won’t accept Safari anymore.

Safari for iPadOS can be reinstated using the App Store:

https://apps.apple.com/gb/app/safari/id1146562112

Safari is an integral element of iOS/iPadOS - and cannot be updated independently of the OS. If your iPad has been updated to the most recent version supported by your iPad, then Safari is as up-to-date as is possible.

However, some websites incorrectly identify your iPadOS Safari User Agent when used in one or other of its browsing modes - of which their are two - these being Desktop and Mobile.

It’s easy to switch between modes if a website isn’t functioning correctly. From the desired web-page, touch the aA icon at the left of the Address Bar; this will reveal a menu. From the menu select Website Settings, then select (or deselect) Request Desktop Website, then tap Done. Now refresh the webpage.

The chosen setting will be saved for the selected website - and can be simply reversed if needed.