Wave patterns:
Pushing the wave and controlling the enemy is the primary job of any mid lane champion, especially a control mage. Best way to achieve this as Hwei is to spam W3+Q3.(Mana refund paired up with zoning and wave shred)
Ideally we place our Q3 to touch the enemy champion as well to utilize our Arcane Comet, First strike, Scorch etc. Now as we master Hwei we get more comfortable and better at putting enemy into our Q3. We can do that by using E2 to root/zone them in or E3 to pull them into the fire.
W3->Q3
W3->Q3->E3
W3->E2->Q3

Poke/Execute patterns:
Poking and executing is something we do when we are already ahead or in a privileged position. Once we shove enemies under the tower or get them low we can start spamming the Sun strike combo W3+Q2. This is the best way to poke and kill enemies while refunding your mana. More complex combos involve rooting/zoning enemies into our W2 execution.
W3->Q2
W3->E2->Q2

Lane Combat Patterns:
Your lane bread and butter combat pattern with be your Q1. It is the most straight forward ability in your kit and it's fairly easy to hit or splash off of minions. If enemy approaches your melee minions we can self buff into the splash W3+Q1. If they are totally beyond the wave we can even begin with a fear, as long as we have clear line of sight W3+E1+Q1.
W3->Q1
W3->E1->Q1

Pick patterns:
Picking enemies off in the jungle will be your number one way to snowball and win the game. If you are a control mage and you are doing your job well enemies will be pushed in and have no access to the river and jungle. Their map will be dark and you will take advantage of that. Using Control wards you can make sure you are not visible while the Yellow Trinket will give you the necessary vision to execute a play. If enemies are wandering off into the dark make sure to be there and combo them. We start with self buff for maximum damage output into fear, then we drop our ultimate. W3+E1+R + Q1/2 (We will use Q1 if enemies are close and flashless, while Q2 if they are far or they flash away)
W3->E1->R->Q1/Q1

Defensive patterns:
Defensive patterns are employed when we have to hold our ground. Two most common cases are: getting jumped on in lane by an assassin and getting contested in the river on an objective.
In the lane case (1v1 or 1v2) we will drop a shield on ourselves which is very powerful, especially early game. Then we proceed to line up our fear into chunk
W2->E1->Q1
In the river case(5v5, 5v4 etc) we will use the shield as well as it's value only grows per number of team mates. Then we will use our zoning tool, the eye.
If enemies step into the root we will use out full combo to destroy any chance of contesting the objective.
W2->E2->R->Q1/Q2/Q3