Has any one an idea of how to reinstall AHT in Big Sur?

My external ssd doesn't show up on the desktop. It is visible in disk utility but it has become unwritable. I can't repair, split or erase the disk' Does anyone have an advise for this issue?

I am running a MBP intel with macOS 11.6.2 platform and 2 Thunderbolt ports. I travel much and sometimes Wifi is not available and I have to use the ethernet cable. Before upgrading to Big Sur it was automatically connecting and working well. But now the thunderbolt bridge does not connect although when I look into About this Mac, System Report, it says connected. When I switch the cable to the other port, it also reports 'connected' to the other port in the System Report. But, I have no internet connection because in the System Preferences-Network panel it reports: Thunderbolt Bridge not connected. How should I configure this? Could any one help me out?

You do not have permission to open the document “256x256_OSX.png”. after the update to Big Sur I am unable to open some files. I have tried to reset permissions in Finder/Get Info but to no avail

Running Big Sur 11.1 cannot go into the Recovery Mode. Anyone tried it? It stops at the very beginning with a warning sign and error 5101D