Matchup as well as personal preference.

AD champions in general, Talon and Zed are some of the hardest counters, mid lane Tristana too, also mid lane Lucian. I guess the most common counter would be Zed. In general though there's so many easy counterpicks to Kassadin that you just shouldn't blind pick him if counters is something you're worried about. Instead focus on figuring out which matchups you're comfortable with and saving him for those matchups.

This video is for Fizz but it should help you.

Walls you'd want to Riftwalk over are basically just the same locations you'd want to take blast cones over, but also the spots where I point out potential pink ward locations, if a gank looks free AF and you don't want to risk a pink ward being there and calling your gank out, you can just go through your or the enemy jungle.

Especially on the blue buff side of the jungle that massively extends the time it takes to get the gank usually since you have to walk around such a big wall, but with Kassadin you can just Riftwalk over the blue buff wall so you can ignore potential river wards, and Riftwalk over any wall that would either force you to walk into a common ward spot (like bot lane tri brush) or force you to walk a really long way to avoid it unless you just skip the wall.

Like in that blast cone location where I talk about having a good dive opportunity in the video, if there's no blast cone there at the time you can just Riftwalk that easily. In that same gank path, to avoid potential pinks in the river you can also Riftwalk straight into the enemy jungle from the bottom mid lane brush (ideally you should know you're not about to facecheck into the enemy jungler if you do this).

If this is too risky, you can check the river pixel brush for a pink and if there isn't one, you can walk into the dragon pit and ult over it either into the tri-brush if ganking over-extended enemies who are too far forward to react in time even if they have the tri warded, and if they're not then you can ult over it into the enemy jungle, far enough away from the tri that a ward wouldn't see you, and go over to that blast cone location and either take the blast cone if it's there or ult over it again.

There are too many of these kinds of things to explain over text, I just wanted to give you some examples of how you can abuse your mobility to avoid common ward spots. This warding guide should give you an idea of common ward spots for mid lane/jungle and experience should tell you where side laners tend to ward, use this knowledge coupled with some creativity to figure out the best ways to use your ult to avoid vision.

But also remember that it's not necessarily always the best choice to avoid vision. Maybe you shove out mid and there are no great gank opportunities but you have nothing better to do so you may as well try; rather than avoid the river in case there are pinks there, walk through the river and look for pinks. If there are any, clear them out to deny enemy vision, a reward of its own.

Since your gank wasn't guaranteed to work out anyway, clearing out enemy vision may be a more valuable act anyway. The paths which are designed to try and ignore enemy vision as much as possible are only for when you really want to get the gank off, if you know it has a good chance of success. Otherwise, clearing out vision is a good alternative.

You definitely don't want to use Sorcery primary, Electrocute and Fleet Footwork are better keystones.

It simply takes too long to scale up, Kassadin already takes a while to come online and Tear of the Goddess delays that even further for mana that's usually overkill, and then on top of that it means you have to skip out on either Rabadon's Deathcap or Void Staff.

Summon Aery is better since Kassadin can't easily proc Electrocute until level 6.

It's actually what you're meant to do, I hadn't realized that I haven't updated that.