Hi and welcome to the thread, I don’t have direct experience on some of the questions you posed but I’ll do my best based on my understanding/speculation and I’ll indicate so. Hopefully the others who have direct experience will weigh in!
(A)
When I applied for the TARC Copy (aka “Exit & Entry Permit and TARC-Copy 入境證及居留證副本” ) from the US, my NWOHR passport was valid and it already had yellow entry permit taped inside it. That said, I didn’t see in the requirements for the TARC Copy application that it requires a valid NWOHR passport, or an entry permit, for that matter. What it requires is a document that can prove your Taiwan nationality, which according to their list could be a NWOHR passport or any of the following pasted in the blockquote below, but I suspect that it might be possible to start the TARC Copy application with an expired passport as well, because the issuance of the passport itself to you should in my view be sufficient proof of your Taiwan nationality. The TECO officer who handles your TARC Copy application could disagree, of course, and might require you to first renew your passport, but to me there’s no harm in trying or at least asking if you could submit that expired one first to save time while you apply for a renewal (assuming you have none of the other proof documents). I’ve read that in fact, some TARC applicants skip the passport application step entirely until after they’ve entered Taiwan using the TARC Copy. It might be worth noting here that the piece of paper that results from the TARC Copy application process is itself called an Exit & Entry Permit, meaning, I believe, that it could be used to as a one-time entry permit into Taiwan without the NWOHR passport, though for completeness I will also add that if you were to renew and enter Taiwan with the NWOHR passport and the TARC Copy, both your passport and that TARC Copy will be stamped by the entry official.
“The passport of the Republic of China or certificate as sufficient to prove the nationality of the Republic of China, e.g. nationality certificate, certificate of overseas Chinese (excluding the certificate of Chinese ethnicity issued by Overseas Chinese Affairs Council) or military certificate previously issued by Department of National Defense”
三、我國護照或足資證明具有中華民國國籍之文件,例如國籍證明書、華僑身分證明書(不包括檢附華裔證明文件,向僑務委員會申請核發者)或國防部核發本人之前國軍官兵證明文件等。
I did not do this but my guess would be no. The TARC Copy application at my TECO was handled by what TECO called the “Immigration Department” – meaning, I surmised, that it was the side of TECO that had NIA officials staffing it. The passport renewal and visa applications, I believe, were handled by the “Consular Department” – I think that’s the BOCA side of TECO. I believe the yellow entry permit might also be part of the passport side but don’t quote me on that. Also, I am less clear on how the yellow entry permit factors into all this if you are ultimately granted the TARC Copy, because you’d be entering Taiwan initially with the TARC Copy and not the yellow entry permit. The yellow entry permit might not be necessary at all unless you plan to enter and exit Taiwan multiple times before completing the residency requirement to get full nationality with household registration.
(B)
I believe the TARC Copy serve as your one-time entry permit, so as mentioned above, the yellow entry permit might be good to have if you anticipate having to exit and reenter Taiwan before you get full nationality with household registration but probably not strictly necessary. I vaguely recall that when I applied for the passport initially, the yellow entry permit is just a free add-on option – maybe a checkbox to tick on the passport application form. Perhaps the passport renewal application might have that as well?
( C )
Check out this chart if you’re able to read Chinese. Based on what you said, I believe you’d be applying under AF353, which is the lineal blood relations category. On the right column, it clearly is an “OR” – i.e., the original copies of your parents’ national ID or the the original Household Registration Booklet or the Household Registration Transcript issued within the past 3 months. But, to properly set your expectations, notice also that the end of that sentence unfortunately includes a catch-all of AND for any document that will serve as sufficient proof of lineal blood relations.
Sadly, this in practice opens the door for your TECO officer to ask for any and/or all of the documents. This happened to me, and no amount of logical pleading on how difficult it would be to obtain some of those listed documents in their original forms helped. YMMV!
(D)
I agree that it’s risky, and I would not mail the originals of anything unless you’ve absolutely confirmed with the officer accepting your application that they’re required and discuss a plan of how to get those safely back to you. I am aware that some of the TECOs, I want to say SF’s, said on their websites that they’d be willing to take a passport copy instead of the original during COVID, but I am not sure how widely they’re willing to apply that rule so best to ask specifically. I suggest calling your TECO’s info line and ask to speak with someone who can accept a TARC Copy application (僑居國外之臺灣地區無戶籍國民申請在臺灣地區居留). Hopefully they can put you in touch with the specialist and you could arrange directly to meet up with that person. At my TECO, my direct interfacing officer was very helpful and flexible on when I could go back to TECO and supply the various documents that they said I was lacking.
(E)
No need to notarize or translate but yes, it does have to be authenticated (US$15). In order to submit the health check for the authentication step, it has to be sealed with the clinic/hospital stamp over the sealed flap of the envelope. If you’re unable to arrange that, my understanding is that you could in lieu have the health check notarized, but I think I mentioned in a prior post that I don’t understand how that works, because I thought a notary public’s function is there to witness the authenticity of signatures, and in this case, it would be your doctor signing the health check form, not you. So I’m not sure if one would be able to drag a notary public into a doctor’s office to do this, but maybe big hospitals might have notarization departments or maybe if you happen to have a relative who’s a notary public you could bring along or something. The FBI check / birth certificate / marriage certificate for authentication did not need to be sealed, but note too that you’d be authenticating each of these 3 documents essentially twice – because there’s the English original and also your self-prepared Chinese translation.
(F)
Yes. Oh, so I’ll add to the above here that document authentications are handled by the “Consular Department” (at least at my TECO). This was why the documents had to be first authenticated before they could be submitted to the “Immigration Department” and it couldn’t be done in one fell swoop. For me that meant more trips to TECO, and I’m not sure how that would’ve worked for mail-in applications. It’s possible your officer might be willing to liaise with the folks responsible for authenticating, and maybe your officer could just collect multiple layers of fees from you and distribute them to the required departments accordingly, but that did not happen for me and I was required to do the authentication of documents steps first before I was allowed to submit the TARC Copy application. Budget extra time for that, as I believe COVID has significantly slowed down processing times for authentication of documents. When I first started, I was allowed to pick it up in one week, and by the end of my process, it stretched to 2 weeks with pickup hours strictly limited. And this was without mailing delays!
(G)
We’re not at this step yet so I hope others who have already finished can confirm, but definitely not (1) for us, but possibly (2), and we hope it’s not (3). Not sure what your family’s moving timeline is but one big consideration would be entry visas for your US-passport holding spouse and child if you plan to enter while the COVID restrictions are in effect. I laid out how excruciating it was in my last post regarding obtaining a spousal visa just to be able to enter Taiwan together, and unfortunately for us, a Resident Visa was denied as an option, which would’ve made it easier/cheaper to apply for the spousal ARC. Still, from what I’ve read so far, I believe (2) is possible, it will just take longer, as I learned that exchanging the TARC Copy for the real TARC is not a same-day thing and is likely to take up to 5 business days. By the way, I think the TARC Copy must be exchanged for the real TARC within 15 days after entering Taiwan, but I believe the time limit has been extended due to COVID quarantine requirements, and it might now be 30 days. Still, I don’t know how that interplays with the spouse applying for the ARC and if there are timing restrictions for that, too. Again, if anyone else has completed this step recently, it would be valuable insight to add to this thread indeed!
Best of luck! Feel free to PM, too, if anything I wrote above is confusing.