iMac not starting up, grey screen, question mark folder, no access. Help please

Hi,

Earlier this year, I installed a new 1TB SSD into my iMac to replace my 3TB fusion drive which had died. It turned out the new drive was too small to restore from backup because I had so much stuff on it so I ended up just installing an external SSD...also 3TB, which handled everything fine.

It's been working OK, but sometimes it just shuts down randomly (not often thankfully)...occasionally when this happens there are problems starting it up....in Disk Utility the start up disk can't be found...but this is not always the case....after a couple of attempts the mac usually eventually finds the right disk and all is well.

Today however, I decided to shut down the imac as i'd had it open for weeks without giving it a rest. Unfortunately for a few hours I've not been able to start it up again. I get the grey screen with a flashing folder with a question mark which lasts 15-20 seconds, then a 'no entry' type sign for 15-20 seconds and then we're back to the 'prohibited' icon...and this alternation continues. So, it looks like the startup disk can't be found.

When i go into Disk Utility, however, it says the Mac osx base system appears to be OK. However, when I run repair disk (on the external SSD) it says 'Error: partition map check failed because no slices were found'.

What can I do? Any help appreciated.

The Imac is late 2012....and can take up to OSX Catalina (which is what I was using)

Here are some photos of what's on the screen: