I don’t think iCloud will be of much help in this case, due to storage capacity limitations of the cloud. Although keeping a copy of just your “favorites” photo album there might be a good use of it – keeping within the storage constraints.
Unfortunately, Photos just isn’t as stable or as performant, or as integrated with iCloud as it should be, considering how long it has been around and how much Apple likes to pride itself on the “it just works” mantra. I’m not saying you shouldn’t use Photos, just that you should probably use it in limited scope and not rely on it too much. Some prefer Image Capture as an alternative for just copying photos over from your mobile devices. The important thing about Photos is that has a checkbox option for deleting photos from their device of origin once they’ve been successfully copied over. Make sure you’re using this, or you won’t be freeing up any space for new photos on your source devices (iPhone, iPad, etc).
That error message is due to memory (RAM), not storage issues. It may be caused by Photos, or it may be caused by some other app. Further probing is needed. But either way, it sounds like you’ve got problems with your Photos library that need to be resolved first.
One thing you can do instead of trying to open the corrupt library is navigate to your .photoslibrary file (it’s actually a package, not a single file) in Finder and Show Package Contents. This will allow you to access your actual photos. They are contained in subfolders inside. This is one thing the designers of Photos got right – you can still access your photos as individual files.
Next launch Photos while holding down Option and when prompted to “Choose Library” click on “Create New…“. Since you mentioned not wanting to store your photos on your Mac’s internal hard drive, use an external one. Even if your MyPassport drive has the capacity for it, I recommend using a separate drive for this. Redundancy for the sake of backup is a very good idea.
Drag files or folders of your photos from the subfolders of your .photoslibrary onto the Photos icon on the Dock. This is similar to doing File → Import… from within Photos, except that when selecting files to Import, you cannot see inside a package. Dragging from Finder gets around this limitation. I expect many aspects of the structure of your old Photos library will not be preserved (such as favorites, albums, photo edit settings, face data, etc). But your photos themselves should be salvageable.
Why Photos libraries get so easily corrupted, I do not know. There are lots of aspects of the Photos app that could use improvement, as I mentioned. You might also explore whether there are tools that can “repair” a broken Photos library, but use caution. Pulling from the package contents and starting a fresh library is the surest bet, in my opinion.
Finally, moving forward, consider buying an additional drive to back up this new library you will presumably continue to add photos to.