There are a couple businesses within Taiwan Taoyuan International Airport that provide printing / photocopying service.
7-eleven / ibon Kiosk in Terminal 1
The 7-eleven in Terminal 1 (B1) has two ibon Kiosks, a self-service machine that supports printing and scanning of documents (instructions here):
You can print out any documents or pictures saved in ...
According to TripAdvisor, the 7-11 convenience store has printers where you can print, scan and fax.
I can't really confirm based on their website (in English, there is a Taiwan website too) because it's not explicit on there but there is a phone number to the terminal where the store is located that you probably can call to be sure.
Lufthansa has made a statement about this:
Information on the carriage of Apple MacBooks
Apple has recalled certain 15 inch models of Macbook Pro laptops sold between 2015 and 2017 as a result of a battery defect. If the battery of those specific recalled models were not replaced by the manufacturer, the passenger will not be able to carry the laptop ...
There should be no problem for you in taking your laptop and three tablets into the US. You've mentioned in the comments that "...all of them are much older than 1 year..." thereby the customs officer more than likely won't even look at it twice.
You are visiting the US, you will leave and take your things with you.
That means that you do not 'import' the electronics, you 'temporary import' them.
This means that you look at different 'maximum allowed' level.
Basically, as long as the customs officer is convinced that you will take them with you when you leave, there is no hard maximum. The harder ...
But can they really refuse to load my baggage because of that?
That's irrelevant. They have in fact done this. You'll have to deal with it.
How did my bag even make it to Beijing then? It passed through customs at A, and made its way to Beijing without any problems.
Your bag did not pass through Customs in A. It passed whatever security screening exists ...