You can install better alternatives using two ways.
There is the appstore where you can simply search for Opera or Firefox.
The second way is using the terminal.
Install Opera (recommended): sudo apt-get install opera
If it doesn't work,try it with opera-stable,I'm not sure about the package name
Install Firefox: sudo apt-get install firefox
I recommend using the appstore because you don't seem to know much about the terminal.
If they both don't work,there are even more alternatives.
One of them would be Midori: sudo apt-get install midori
Or QupZilla: sudo apt-get install qupzilla
I'm not sure if the last two are available in the official repositories but here the terminal method is recommended because there are more programs and it is more likely that you will find it there.

2001, well, thats a bit old haha... Chrome won't offer support for such old hardware, and Chromium based browsers (Chrome, Opera, Vivaldi, Brave), probably won't offer suport, too... Anyway, as your hardware must be limited, ram, disk, you can try light browsers, like Midori, Min or Pale Moon, greetings.

Thanks for your responses! I tried using the software center, but every file fails to install. I also can't open the Control Center. Any idea why this happens? I was able to get Firefox through firefox.com and had to install via the terminal.

The problem maybe is the hardware, how much ram you have and how much is consuming Deepin on idle?, terminal is more reliable for installing when resources are low, but first, please tell me your pc specs, so I can know how much free space you have (cpu, ram) to work. Maybe you need a light distro for your hardware.
The minimum requirements of Deepin are: 2ghz dual core processor, 512mb of ram, and at least 5-10GB of disk.