You have plenty of headroom on your recording, so I wouldn't add any compression on the recording phase unless you're REALLY familiar with how compression works. Artistic color choices aside, you'd only really need to do that if there were extreme volume issues (like you were working on a script that required some yelling or screaming) so you don't accidentally clip and ruin a take. Other than that, it will give you (or the mixing engineer) far more flexibility if you leave the compression for post-processing.

If the audio is being sent to a mixing engineer, you should be good to go. If you are uploading things yourself, you'll probably want to "normalize" your audio. This will take the loudest part and set that at the maximum volume before it clips. That way, your audio will make use of all the headroom you've got (all the vertical space in the waveform). If you are sending it to a mixing engineer, don't normalize. They'll typically appreciate being able to take care of that themselves.

The recording sounds pretty good! You could probably get a little closer to the mic so it picks up less of the room, and then crank your gain down accordingly to keep the levels from clipping. The gain is set a little high right now which makes the mic a bit more sensitive allowing it to pick up sounds that are bouncing off the walls or ceiling. One of the benefits of using a preamp/audio interface like this is you have more control over the signal as opposed to a mic with built in pre and converter. Get a little closer and turn the gain down to compensate and it should help remarkably with the ambient sound (although it's honestly not terrible). If it remains a problem, you could buy (or pretty easily build) a reflection filter. I could step you through a few options if you want. Audacity is fine for recording audio. The app that you use generally won't make a huge difference when it comes to recording. There are slight differences in workflow when editing, but even then, they all basically do the same things.

It seems like you're recording in stereo which is why it's only coming out of the left channel. At the top of audacity there should be a dropdown between the input menu (icon of a mic) and an output menu (icon of a speaker). If that middle dropdown says 2 (Stereo) Recording or something like that, you'll want to change it to Mono.

Feel free to DM if you have any questions or want to chat about it further.

Still getting the mono audio.
To answer your question, you can add a bit of compression during the recording, and add some more during the mixing stage. It's just there to smooth out the peaks and valleys in your voice or instrument.

Edit: I used to have a ridiculously expensive Darkglass pedal that had 3+ different compressor models on it. Way too much for someone who doesn't know what he's doing, as far as compression goes.
I don't know any programs, as I don't have a PC for recording at the moment. It's actually something I'm working on right now.

It looks great! How much did the entire package cost? Pop filter, microphone, and that box with reverb and other settings.

Sounds pretty good! However the room you're in is very reverbrant, might wanna treat the walls with some foam, or even blankets, bedsheets and other household items to absorb any possible echo that your voice might make.
Second, the audio is completely panned to the left side.
I would also recommend compressing the audio, using a compressor, they come built in with all/most audio programs, this will level out the all the audio and make it sound equal, and not too quiet at parts, or not too loud at parts.
There ya go! Hope any of this helps, and apologies for going on a long winded blabber lol

My Left ear enjoyed this! I think there may be an audio error and it's exporting for only one side of the ear. Other than that, it sounds pretty good. You should stand/sit a little closer to the mic too. If you're new to audio mixing, audacity is good to start with, then move on to adobe audition and the other stuff corey reccomended.