Trip from Taiwan to Shenzhen > Hong Kong > Taiwan

Yes, your itinerary is definitely eligible for 144 hour visa free transit valid for entire Guangdong province, assuming that you are a citizen of Luxembourg. So, you will not be limited just to Shenzhen city boundaries, but you will be able to visit even other places within the province. Please, just avoid possible misunderstandings because some officials could interpret your journey as if you wish to obtain a 5 day Shnezhen visa, but this visa is not what you are looking for.

I suggest you to use a ferry from Shekou port to Hong Kong provided by CKS - Chu Kong Passenger Transport that operates on the route from Shekou port to Hong Kong. The years long practice shows that Chinese authorities prefer ferries over other options for some reason. Also, have in mind that you will have to buy your ferry ticket and to print it out in order to have it ready to present it to relevant authorities. You will have to take exactly that ferry you have bought your ticket for.

After you have exited to Hong Kong, you can proceed to any direction of your choice.

Hello there,

For this case, can I stay in Hong Kong for another 3 days?

For example:

5/6 Taiwan to Shenzhen
5/10 Shenzhen to Hong Kong
5/13 HK to Taiwan

Of course you can. You can stay in Hong Kong even more because Hong Kong is excluded from the mainland China visa and other rules.

As I have written in the above post, after you exit from mainland China (Shenzhen in this case) you can stay and go wherever you want.

The rules that we are talking about are valid for mainland China only.

Just have in mind to take preferably a ferry from Shenzhen to Hong Kong and to have that ticket with you in hard copy.