OP: Does Viññāṇa generate Nāmarūpa in the sense that would make "uploading concsciousness" impossible?
Yes, as mentioned in dependent origination Viññāṇa (consciousness) is the main cause for Nāmarūpa (name and form) to be arisen. (Note: there are many causes other than Viññāṇa which help Nāmarūpa to be arisen. Viññāṇa is also be the cause in different ways/conditions. So each of these can be considered as a different cause.)
Computer programs are dependent on computer hardware but computer hardware are not dependent on computer programs. There's no mutual causal relationship between hardware and software. But as mentioned in many suttas, there's a mutual causal relationship between Viññāṇa and Nāmarūpa. (SN 12.65 - Nagara Sutta, SN 12.67 - Nalakalapiyo Sutta)
Yes, it's impossible to upload consciousness into a computer. How could we make something to arise in an entirely different environment (without all the required conditions) which it supposed to be.
OP: Wouldn't every Buddhist say that pots and trees are mental constructions, so that, even if granted concrete reality, as in the Sarvastavadin school, they don't exist from moment to moment?
According to Teravadins, all conditioned things exist in this very moment. But not in the past (already decayed) not in the future (yet to be arisen). All the conditioned things exist as a stream subjected to momentary uppada (arise), thiti (exist), and bhanga (cease).
Sarvastivadins have a different idea on this. They believe all exists (sarvām asti) and holds the idea every dhamma exist independent of time (past, present, and future). Suppose you cut down a tree and made a table out of it. According to Sarvastivadins both tree and table exist.
OP: But should the Buddhist claim it's not merely opaque but impossible, especially due to mind-body dualism?
I have already discussed this in the answer to your first question.
OP: Does rebirth consciousness actually form the new body (and mind), in the 12 links of dependent origination?
Yes, according to Abhidhamma, the re-linking consciousness causes name and form at the reappearing in the following way.
Re-linking consciousness be the cause for vattu-rupa with 9 conditions.
- Co-nascence condition (Sahajāta paccayo)
- Mutuality condition (Aññamañña paccayo)
- Dependence condition (Nissaya paccayo)
- Kamma-result condition (Vipāka paccayo)
- Nutriment condition (Āhara paccayo)
- Faculty condition (Indriya paccayo)
- Dissociation condition (Vippayutta paccayo)
- Presence condition (Atthi paccayo)
- Non-disappearance condition (Avigata paccayo)
Re-linking consciousness be the cause for remaining rupa-kalapa (bundles of form) present at the reappearing moment with 8 conditions.
- Co-nascence condition (Sahajāta paccayo)
- Dependence condition (Nissaya paccayo)
- Kamma-result condition (Vipāka paccayo)
- Nutriment condition (Āhara paccayo)
- Faculty condition (Indriya paccayo)
- Dissociation condition (Vippayutta paccayo)
- Presence condition (Atthi paccayo)
- Non-disappearance condition (Avigata paccayo)
Note: This is what I understood. I may be wrong but not Dhamma.