What to use for a matcha whisk?

The bowl isn't absolutely essential; it's part of the aesthetic. The shape does serve a purpose, as most of them have nicely curved bottoms that will minimize the chance of the powder from clumping near the edge of the bowl.

I've used a normal whisk when preparing "matcha latte" drinks for a client of mine back in the day. There's an advantage to having the 80-120 "tate" (bristle?) because they make it easier to break up beads that form as moisture contacts the tea. But a normal culinary whisk will do the trick, perhaps with a bit more work.

I don't see how the silicone brush would help whisking; they tend to be pretty floppy (and mine has occasionally had some of the silicone strands break off when I've used it for brushing food).

Yes, you can likely use a regular whisk, it should work fine - it's not much extra trickiness compared to other powders which threaten to clump up.

I tend to make matcha in paste-and-loosen form - a paste doesn't have enough liquid to let clumps slide around instead of mix in, and it's easier to loosen a thick paste to a solution rather than gradually than try to whisk a dry powder into a thin liquid. With the thinning a paste method, it is fairly easy to use spoon, fork, butter-knife, chopstick, or, well, whatever.

Since I usually like tea a bit on the cooler side, I sometimes loosen it up with cold water, so it doesn't over-steep before cooling enough for me to drink (and sometimes the reverse, use less hot water and add cold water for the rest to end up at drinkble temps fast).

As for your update, yeah, electric milk frother works. Pretty well, actually. I tend to use it if I miscalculate the initial mixing, and it smooths lumps really well. Just like an immersion blender, it works best if there's enough liquid, and enough room in the vessel, to let the contents slosh about rather than spatter all over the place - maybe liquid an inch over the head at a minimum, a couple inches is better, and a couple more inches of bowl-space to accommodate it sloshing or frothing up a bit? Or, given how tiny the head is, total of a half a glass or mugfull, mix well, add the other half of the liquid which mixes smoothly since the lumps are ded.

If you're really into matcha, then you should be picky about getting a dedicated bowl and whisk. Those bamboo whisk can mix the powder more fine resulting in a more thick and creamy matcha. Round bowls also help, because it fits the whisk better. You can mix more conveniently in it compared to a mug.