Please can someone help me understand?

Part 1:

Unfortunately, your first segment is not eligible for any kind of visa free transit and it requires a visa obtained in advance. Simply speaking, when you travel on 144 hour visa free transit you are not allowed to have two mainland Chinese destinations (landings) of any kind in a row. As you can see, you plan to have Beijing and Shenzhen in a row. You are informed that in China all the immigration formalities are done at the very first landing, so your flight from Beijing to Shenzhen is considered as a domestic flight and 144 hour visa free transit does not allow it.

If you want to stay in Shenzhen and Guangdong province in general, you will have to fly directly (nonstop flight) from some country to either Shenzhen or Guangzhou and then exit toward the Philippines or Hong Kong. This is the only eligible way how you can do that. The exit to Hong Kong is easy part because you just need to buy your train ticket before your departure to China and have it at hand because you will be asked to present it as a proof that you will be really in a transit. Also, you will have to take exactly that train you have bought your ticket for.

Your return journey is definitely eligible for 24 hour visa free transit and here you do not need any kind of visa.

Part 2:

If I may suggest you since you seems to be traveling to Shenzhen only. So, my suggestion is that you fly directly to Hong Kong and then to enter Shenzhen by obtaining a 5 days Shenzhen visa on arrival at the border crossing. Also, you can take a ferry from Hong Kong Sky pier terminal directly to Shekou port in Shenzhen where you can apply for that visa. You should just have in mind the opening hours of visa offices at relevant border crossings that are only border crossings to offer such a visa:

Luohu Port 9:00 - 16:30
Huanggang Port 9:00 - 16:30
Shekou Port 9:00 - 13:00 & 14:30 - 16:30

The price for this visa on arrival is affordable amount of 130 CNY. After your stay in Shenzhen you can return to Hong Kong by direct train from Shenzhen.

Thank you so much for your guidance! I appreciate your advice :)