My knowledge level is improving but still relatively low so take my two cents with a grain of salt:
Your suit is not bad for the price and the first make. I actually like how it lays in the back. I agree that the jacket may be a tad longer but not much. The most glaring adjustment to make the next time is the button position. It looks too high in the photo, and this makes your upper half look small, and draws too much attention to your mid section. I would prefer the lapel to run longer and the button to be lower. Maybe this would also allow for better shaping around the torso.
As for the pants, I agree with the other comments. The seat is tight and pulling on the pockets, and the pants need to be shortened. These should be easy adjustment for your tailor.
Regarding buttons, my experience is that many tailors, even ones at high price points, often go with plastic buttons if you don't ask for specific quality ones like those made of horn. I've never understood this. It seems better for the house brand and for the customer to use better ones and just pass on the cost to the customer. It's not much in the total cost of the suit. With a discount tailoring service like you are using, you will most certainly get cheap buttons if you don't ask for quality ones or provide them yourself. There are plenty of tailors of course who really emphasize the trimming quality but you can't assume they will even at high price points.
If I were you, I would post this in the tailors thread and get professional feedback. Despos often weighs in and has an expert for eye for the type of questions you are asking.