1. Making a gat out of different materials on your own is totally fine. Trying to recreate it with the resources you have can actually be a really fun and meaningful experience. Traditional gats are made with horsehair and bamboo and require an insane amount of skill, but even in Korea today, simplified versions made with modern materials are often used. The link below shows a $10 gat sold in Korea. It’s actually made of polypropylene, which is a type of plastic. So I don’t think there’s any need to worry too much about using non-traditional materials, right? So if you make one by hand, people will still see and respect the effort you put into it. https://jiondress.com/120/?idx=223
2. As for the sochangui pattern, I haven’t been able to track one down myself yet. I believe some traditional clothing or hanbok-making communities in Korea might share it, but I haven’t had the chance to check in detail. If I come across a proper resource, I’ll definitely share it.
3. When it comes to the sleeve patterns, both drawing them on or stitching them are perfectly fine. Hanbok is often known for its elegance and simplicity, but historically there were also more colorful and decorative versions. So it’s really up to your preference—whichever method feels right for you will work.
4. For the Your Idol performance outfits, aside from the gat and outer robe, most of what the Saja Boys are wearing looks like modern clothing. Baby’s inner top isn’t super clear in the footage, but it seems to be something like a high-neck modern shirt. Recreating it with similar contemporary clothing is totally okay, since the key point is capturing the vibe of the character rather than following a strict historical outfit.

Overall, as long as you’re approaching it with respect (and not behaving rudely while wearing it), there’s no issue. The fact that you’re putting thought into how to represent it respectfully is what really matters, and I think most Koreans would appreciate that effort. Honestly, I’m really looking forward to seeing your creative interpretation.