Preware is an app that functions in a similar way to other onboard app catalogues or software managers. There are a number of repositories of apps on the internet & these provide feeds or listings of their content. These feeds are displayed in the app and selecting an installation package (IPK) causes that package to be downloaded and the app to be installed. Preware can also install IPKs that are stored on the device in the way that WebOS Quick Install (WOSQI) installs IPKs stored on your computer via the USB cable. This is known as sideloading (this term is often used to mean installing apps outside the official app catalogue, but now there is no official catalogue). You have sideloaded Preware onto your tablet with WOSQI.
It appears you have already installed 18 apps by one or both of the methods above. Tapping through that information will show the names of the apps and then descriptions with buttons to install, update, launch and remove (depending on status).
One of the available feeds is the one from this site, which is probably the largest. Click the 'apps' button at the top of this page to see the app gallery. You could download an app to your computer and install with WOSQI or transfer it to the TP via USB & install it with Preware (swipe down from the top left to see the app menu for this option & others including managing feeds). The easiest thing to do is probably to just download & install directly in the Preware app.
That's the simplest explanation I can give I think. In addition to apps, you can also install patches which are modifications to apps or webOS itself. As this system has been unsupported for some years, any fixes have been supplied by experts in the community. Some are packaged for Preware, but simple patches are often found on threads in these forums and need to be installed with WOSQI or Internalz Pro. Patches can also customise system behaviour. The biggest modification is probably Luna Community Edition which packages many improvements to the TouchPad user interface and was made with support from HP.
There a list of important fixes in the service pack link below. The other links can offer you useful info such as apps that are no longer working properly. Some of these have fixes available.
Regarding the browser, it is old and not bad, but some complex websites can cause issues. There were a few browsers or upgrades available in the official catalogue. There is no version of Firefox available. The browser is a big complex program & it is unlikely there will ever be a new one arriving as it would require a big technology update. There is a new, home-brewed version of webOS called LuneOS, based on the open-sourced code. It's still under development, but the browser is reportedly pretty good. This runs on the TP and you can also install or dual boot the open-source version of Android which may also allow the use of more modern browsers.