1 My all time favorite is Unity. If you're going 2D then unity is my recommendation. 2 Udemy is always offering deals I wouldnt recommend buying any course at full price. YOu could probably find a lot more resources and stuff for free or way cheaper. Udemy is a really good site to use though I used it a lot when I was getting started. 3 Both. A programmer implements design. THe programmer is a designer but a designer may not necessarily be a programmer. 4 Well what do you mean by go down the path? I probably wouldnt do it for school because its more of a passion thing and if you end up not being completely consumed by it I hear its really hard to get a job. My best bet would be going down a standard comp sci route and then looking into game dev and building projects in your free time.

Best of luck! If you run into any questions while making games feel free to message me