You can definitely use fresh shiitake mushrooms instead of dried, but dried will give the soup a better flavor. Cold water also works to soften the dried mushrooms, it just takes longer. The amount listed for mushrooms (3/4 ounce) should be about 6 mushrooms.
Use soft tofu for this. Use Chinese black vinegar instead of seasoned rice vinegar if you can find it. You can use a hot red pepper instead of a sweet one.
This will work with a black pepper or cayenne instead of white pepper, but it's just not going to have the same flavor.
Feel free to customize this--add any other thinly sliced vegetables you like when you add the tofu and other veggies.