He looks healthy and very beautiful! Get siphon as soon as you can if you decide to keep the filter. You need to get those debris out from under the gravel. The brown dot probably was his poo.
For 2.5 gall you need to do Twice weekly-1-50% water only and 1-50% with vacuuming.
If the filter "all-in-one" cartridge that is filter floss with carbon inside, just rinse it once a week in tank water or dechlorinated water. Most of the filters use those kind of cartridges. If the cartridge becomes too old or starts to fall apart, put a new cartridge in the filter but keep the old one behind it for a week and monitor for ammonia spikes.
When you vacuum-Unplug both the filter and heater-Then plunge the vacuum deep into the substrate and as the mulm/debris clear in a second or two-move and repeat.
Once you refill with like temp dechlorinated water and turn the filter back on the water should clear within the hour-even without a filter the water should clear. If not, you either missed a water change, over feeding or overstocked.
I don't cycle my tanks what i just wrote came from other people instruction. Just want to give you idea what you need to do.
Yes its a few ways to do water changes . You can use the filer and you need to cycle the tank, which i think you don't need it for 2.5 gall and especially that you not experience with it.
Second choice you don't need the filer and you can just do also two water changes(1-50% and 1-100% a week). In this method you don't need to vacuum the gravel .
But if you want filter you have him for about 11 days you need to get siphon as soon as possible to get all debris out. I don't think it healthy to keep it there. You really don't see what under the gravel.
Whenever you buy anything live including the plant always quarantine it first. If you going to get live plant put it in the water with no water conditioner for a few weeks.
And if you will decide to keep the filter you also will need to wipe the walls not sure how often since i don't have the filters in my tanks. But i think the link that you was given has those explanation.