iMac not responding

PS: Troubleshooting the issues: on Mojave

Re: "the mouse does not click at all+

Change mouse tracking, double-click, and scrolling speed on Mac – Apple Support

says:

If you have trouble using a mouse, you can turn on Mouse Keys, then use the keyboard or numeric keypad to move the mouse pointer and click. See Control the pointer using Mouse Keys on Mac.

Change Accessibility Mouse & Trackpad preferences on Mac – Apple Support

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Re: back-up from TM waiting to be restored

If you can't back up or restore your Mac using Time Machine - Apple Support

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Re: "computer freezes and I have to reboot and swap the PRAM"

Wondering if it is a particular app you are using that freezes.

or

Could this be caused by a third-party app (eg: anti-virus, ad-blocker, etc.)

Discussion thread on similar situation: iMac Freezes once a week - Apple Community

or

You might want to try using safe mode, sometimes it helps identify causes, sometimes it rectifiers faults.

How to use safe mode on your Mac - Apple Support

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If needed:

Other sources of support:

You could try reaching out ti the iMac support Team.

There is a "Get Support" link at the bottom of their website (link below)

iMac - Official Apple Support

Hi RafaPapi

Welcome to the Apple Community.

Now I'm no expert in this area, but no experts have replied so far, and your request for help surely deserves attention.

I'm replying with a few thoughts, and perhaps others with more expertise than you or me may join the discussion.

With an elaborate project in mind, and with issues that stop you going ahead.

it would seem updating your iMac to a newer version may be a good step.

Apple support's articxkle: Identify your iMac model - Apple Support

says:

iMac models introduced in 2015 or later can run the latest version of macOS

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Now Apple began transitioning to 64-bit hardware and software technology for Mac over a decade ago

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

says

' in 2018 Apple informed (them) that macOS Mojave would be the last version of macOS to run 32-bit apps

Starting with macOS Catalina, 32-bit apps are no longer compatible with macOS'.

So to update to a recent MacOS version, all Apple apps would update to 64 bit, yet any third-party (non-Apple) 32 bit apps would need identifying.. Any necessary 32 bit apps may be able to be updated to 64 bit apps, others may need an uninstaller from the developer.

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So the current issues seem. to be:

back-up from TM waiting to be restored

the mouse does not click at all

"computer freezes and I have to reboot and swap the PRAM"

Wondering if you are interested in updating, which may or may not fix some issues,

and

how important retrieving the backed-up data is to your upcoming project

or

whether you want to stick with Mojave, and just get the iMac in better working order

All the best :-)