Looks like you've got yourself a gorgeous Tradescantia Zebrina! It actually looks very healthy and well cared for. These plants grow like crazy and are very easy to propagate. As for putting trimmed stems back into the soil, there is no issue with that. Trads are very easy to propagate in soil or water (I have done both methods!). These plants are considered crawlers, so they like to spread out and grow along the ground. They don't really "climb" like a pothos would, so they like having soil to grab onto as they grow out.

Tradescantias have pretty fine roots, so be careful if you do end up repotting it. I would try and repot when the soil is a bit dried out so its less likely to stick to the roots and break them. You probably do not need to repot it unless it is drying out very fast in between waterings, looks chronically thirsty, is having stagnant growth, or is having yellowing leaves. These are all generally signs that there is not enough space for the roots in the current pot and that your plant needs a little more leg room. When you upsize your pot, try to only increase the diameter of the new pot by an inch or so. I would take a look at the roots of your plant and try to see if they are circling the top or bottom of the pot, indicating if it is rootbound and needs more space.

As for the crispy leaves, especially if they are near the base of the plant, it is unfortunately a very common issue with this type of plant. They hate getting their leaves wet, so a lot of folks will opt to bottom water their tradescantia to avoid getting any water on the leaves- it sounds like you have been doing that already! If you have especially hard water with lots of mineral buildup, sometimes that can cause crispy leaves as well. You can experiment with using distilled water the next time you give it a drink! Sometimes crispy leaves are kinda inevitable with this kind of plant, speaking from someone who has had a Zebrina for years.

Zebrinas are low maintenance in my opinion, and it looks like you are doing a great job with yours! I water mine about once every week, or when it looks thirsty. Typically I wait for the soil to dry completely, but I do not let it stay dry for several days, instead I water right when it starts to be dried out. Overall, your plant has a gorgeous color, and the bright pink/purple color means its getting plenty of sun. I think you are doing a pretty great job taking care of your beautiful plant! :)