From Japan to Hongkong to Shenzhen and then Taiwan

Yes, this is absolutely possible. Let's go step by step:

1. Japan to Hong Kong

You can do this without visa and as German citizen, you are fine to stay in Hong Kong for quite a long time

2. Hong Kong - Shenzhen

Here, you will have to apply for a 5 day Shenzhen visa on arrival. The price for this visa is 168 CNY for German citizens and the only drawback is the fact that you are limited to only Shenzhen city area.

3. Shenzhen - Taiwan

You are perfectly allowed to do this, anyway you should have in mind that your fight has to be a direct one and you are not allowed to have any additional landing within mainland China.

As you can see, this is fairly easy. Anyway, if you ask me, I would change the order of the places to visit and I would be doing the following:

1. Japan - Shenzhen (or Guangzhou) - Hong Kong

Like this, you would be able to enjoy 144 hour visa free transit in the entire Guangdong province and after that to take a ferry to Hong Kong. Of course, this requires that you book a ferry online in advance and to have an e-confirmation printed out and in your hand at your check-in in Japan. This is easy and if you want some further explanation, you will tell me.

2. Hong Kong - Taiwan

This is more than easy flight :)

Now, when you know your options, you will make your decisions.