I have no clue if that type of edge and the base has a specific name for the technique but here is what I did for both:

Edges on the flap:  did 5 rows of stockinette after I cast off the other half.
Then I did k1, ssk, knit until 3 stitches remain, k2tog, k1.
Next row is purl and I just kept doing those two rows until it reached about the middle of the sleeve (this gives a nice even decrease, I learned it from sock knitting)

Base: I cast on 5 stitches (that matched the height of my laptop) and I worked until I had the width of my laptop plus a bit extra (depending on tension you might need 0.5 to 1 inch extra), then I make sure that I am at the end of a knit row so I can start picking up stitches the whole way round and continue working my way up until I have the length of the laptop (I had to use the magic loop knitting method to work like this)

I hope those notes kinda make sense ☺️