How do I search and install applications from APT repositories in the Software Center? I searched for applications like "preload" and "apache" and they do not turn up in the search results. However, they are available on terminal "apt search" results.
I downloaded Google Chrome deb and installed it (double click on the file) through the Software center installer. However, it does not appear in the Software center search results nor under the Installed tab. In this case, how do I uninstall it or update it through the Software center?
The Gnome Software Store will not recognize packages installed as .deb self-installers. Nor will it see source installs using Make or Ninja.
Sadly, I know of no way of making it do so.
I recommend that users create a folder for any .deb packages that they install and keep the original .deb package in that folder. This way, you know right where it is if you need to uninstall that software.
Launch that .deb package, then click the Remove option rather than the Reinstall option.
This is a very good question...
I would think they should show up.
While the Gnome Software Store is a good initial package manager, providing ease of use and familiarity, I consider it more of a Stepping Stone for users coming over to Linux. It helps get the person started, but it may be better to graduate to a more comprehensive package manager when the user is ready.
Synaptic Package Manger is my preferred GUI package manager.
sudo apt install synaptic
It can handle just about everything, from installs and removals of any package in APT to managing kernel installs and removals, broken packages, finding missing packages and so on.
Admittedly, I never really use it... I use the terminal for all package management. It is fast, efficient, comprehensive and the easiest to use.
I saw the same, when I search screen record or screencast on Software Center some softwares didn't appear, in fact I searched linux screen recorder on Google and when I searched on Software Center some of the most popular and best ones (for example Kazam and Kooha) they appeared on search results but not when I searched screen record or screencast. Why does it happen?
So would be better if we download Synaptic Package Manager as Aravisian suggested? Because if this store can deliver full search results I'd surely download it , we shouldn't always have to check on Google if there are other softwares that don't appear when I search certain keywords. @Aravisian , do you think there's a way to fix Software Center not showing all search results? On my previous message you can see an example. Users that don't know about this would miss many of the software that they search.
It is not just packages that are in APT and show in terminal or Synaptic that fail to appear in Gnome-Software.
In Gnome-Software, you can sometimes select a package to remove and it says that there is no package to remove. But it shows in terminal and removes in terminal with APT.
Since this is an appstream metadata issue, no one on the forum can "fix" this issue. Only the Gnome Developers can and they were more interested only in fixing anything in Gnome-Software that was going into Gnome 4+.
There are some short term workarounds, like removing the Software Cache files and restarting the software store.
Synpatic is solid, stable and reliable but not as Eye Candy Pretty and Simplified as the Software Store is.
Where Software Store is like the lovechild of Cooper Mini and a Gemlin, Synaptic is a 1978 Dodge Charger.
Some users can feel intimidated by their first viewing of Synaptic. It is nearly as powerful as the terminal is.
I highly recommend Synaptic, but I don't even use it myself.
I use the terminal for all software installs and removals.
It is easy, fast, efficient and Verbose. Even if something fails, it tells me why and usually, it's very easy to know what to do about it.
, we shouldn't always have to check on Google if there are other softwares that don't appear when I search certain keywords. 
you can see an example. Users that don't know about this would miss many of the software that they search.