adobe photoshop lightroom 4 damage computer warning

The first and most obvious question is: are you sure this is really a copy of Lightroom?

While the OS does have hooks to defend against malware, including the ability to block some known-malicious apps, the set you quote does not sound right to me. I have never, ever seen Apple recommend you "... report malware to Apple to protect other users'... especially not without some clear and obvious way to do so.

> 1 - Is this a problem of Catalina not being able to run this application? (64 bit or 32).

Catalina will not run 32-bit apps, so if this is an old version of Lightroom, that could prevent the app from running. However, usually the dialog you get explains that the app is 32-bit and that you should contact the developer for an update (not 'report it to Apple')

> 2 - If so, how do I save the catalog of photographs I have on my Mac? I have the catalog saved on an external hard drive but I can't open that either.

You may need the latest (or, at least, newer) version of Lightroom. Unfortunately this may mean you're locked into Adobe's subscription program.

> 3 - Is there a way to open "package content" in Catalina? I remember having the ability to do that in previous versions of iMac and its various OS's.

The same way as before - ctrl-click on the app icon and choose 'Show Package Contents'.

Good luck determining much from that, though. Few people can decipher package contents to understand what's going on.

> 4 - Or, do I have malware on my computer?

That's possible, but not my first inclination. I would be interested to know where that dialog is coming from, though. As I said, it doesn't sound like an Apple thing, but I might be wrong.

> 5 - If I have malware, how do I purge it?

Start here: https://www.malwarebytes.com

I have a Macbook Pro 2019 16-inch on 10.15.7. I migrated to it from a 2010 Macbook Air that had Lightroom 4. I actually did not expect Lightroom 4 to work on the new Catalina Mac but it does, and I do not get that warning when I run it. Lightroom 4 is very old and I think some features probably do not work under 10.15.7, but I tried various options and it did work for at least the ones I tried. I think it is important that you have the latest version of Lightroom 4. Mine is this (from Get Info on the app):

Adobe Photoshop Lightroom 4.4.1 [908273]

That warning pops up if the software you are trying to use is not properly credentialed. The MacOS is particular about that. That could be due to malware or it could be due to the software being very old and not updated.

It may be hard to update such an old version. Try this link, this did work for me but I did this several years ago (on the old Mac):

https://helpx.adobe.com/download-install/kb/downloaded-older-app.html

For this to work, you need a properly licensed and registered copy of Lightroom 4.

Lightroom 4 is more than 10 years old, you should switch to the latest version, I can still use the old version but I don't use it much and I don't recommend staying with it, actually. I think some options no longer function under Catalina, pieces of Lightroom 4 are 32-bit and just won't function anymore. Eventually there will be a MacOS update or new MacOS and it won't work at all anymore. You can get the latest Lightroom from Adobe for less than $10/month. Yes, it is a monthly subscription but you will be automatically updated to the latest version always. It's how things work now. If you don't want that approach, you can switch to one of a number of Lightroom alternates that can be purchased outright.