I accidentally uninstalled Steam on Software so I reinstalled but won't open Steam but it's running in System Monitor?? 
- Check if you install the right format package (.deb/flatpak)
- Try delete ~/.steam but make sure your games are installed other place.
Where ~/.steam ? and do I after I uninstalled it? I deleted everything permanently.
I installed it on Software, It's flathub.
It's hidden. When there's a dot infront a file or folder means it's hidden.
Flatpak? try clean it from lefterover and then install Steam. You can do this with an app called flatsweep.
Steam, The Ultimate Online Game Platform i downloaded from this link and its has no problems at all
Is it same thing? and say "The packages cache seems to be out of date, Press return to update the list of available packages" should I do it?
I don't know what to choose, offical website or flathub
i would try the website first it seems to work more often then not
I had no problem since years by using and installing steam from Debian / Ubuntu 's repository.
let's see if steam still there by taping this in Terminal
flatpak list --app
then remove the app and data
flatpak uninstall --delete-data <application ID>
you get the ID of the flatpak from the first command
in my case
Then, i recommend you to avoid installing packages from websites ; prefer installing software from APT repository, Flatpak, Snap.
You can "kill" the app from "system monitor".
then install it from Zorin Terminal
sudo apt install steam-installertype your password.
Done