When the skate is off your foot, squeeze the leg end. Does it compress easily or with difficulty? A hockey skate should be quite hard to compress, so that it supports your ankles. If it compresses easily, that suggest that the skates are not supportive enough. It could also be that your laces are too loose. You don’t want them too tight, that can hurt and damage your feet, but too loose is not good. Otherwise the skate should be a snug fit, as you say yours are.
When doing crossovers, if a blade slides sideways that can indicate several issues. A poor sharpening is one possibility, and quite common. If an edge is missing, the blade will slide. It could also be that you are not leaning in to the corner, and hence not using your edges correctly.
Apparently weak ankles is a myth!