Kassadin is a very good lane partner, but you should be able to mid solo with him. My favorite would be to solo because then the other person you're fighting is most likely using more ability power than the rest of the team, your passive helps you a little with this.

The spells are good for the killing part, Exhaust probably won't be used as often as Ignite but at early game when soloing its nice to have them slowed without having to use your Force Pulse yet, you use your abilities then ignite and they're most likely going to die

A good, quick, simple, easy combo for Kassadin is this: Pop in behind the champion with Riftwalk, try to hit them with Riftwalk though, then after that, make sure that your Force Pulse is ready so you can use it as soon as you are behind them, if they're in front of you facing your side of the map, then you have the advantage because they have to go to you to get out. After using Force Pulse activate your Nether Blade and cast Null Sphere, if they're still alive, kill them with ignite or Riftwalk if you can.

Kassadin is a very squishy champion, but his damage output can be massive. Think of him like Malazahar (mind my spellings) if used correctly hes a great champion who can kill a lot of people, but if not used right and doesn't get much kills, a very easy target to take out and most likely will be taken out first.

Thats all i have to say about Kassadin, The Void Walker.