Stats/CDs/ranges is just understanding what your opponents are capable. It's analogous to knowing "Oh, my opponent can CG me between these percents, platform games are a necessity and I should avoid bad shield pressure"
Knowing your role in teamfights is a bit more difficult to describe, but you should know that there are different objectives in fights, such as killing the DPS, or peeling/protecting for your own. Think to yourself "how are they going to kill/focus on my team?" try to counterplay that. Pay attention to who has the most farm on both teams, and most DPS.
Mechanics is all practice. You played smash so you'll get it in no time.
A good trick from DotA to get used to map awareness is peeking at the minimap in between CS/harass. ALWAYS be staring at the minimap when you're not near hostile zones, also be sure to look at the portraits to your left because they tell you when ults are up, what people's health is at, and death timers. OP
Edit: Swarm, elise is a hoe. Hate her lol