I don't know much about Singapore entry requirements, but if they only need antigen test, then do not worry yourselves with trying to get PCR, and just concentrate on the antigen.
You gave yourself 3 weeks for the pass, so that was good. Some people's literally took minutes. Mine was 7 days. The website says if you haven't received a reply in 7 days, then you can contact them if you are concerned. If there is nothing wrong with the details you entered, a phone call (so I hear) will usually get quick results (if you can get through)
You are cutting this quite close. Mine took 7 days from submittal to approval. You need the flight number. I don't know if they actually check that you are booked for said flight though. Also, you need to have your hotel, insurance, PCR tests all pre paid before starting the Thai pass. You also need transport directly from the airport to the hotel (I personally would just book it through the hotel.)
You have to convert (or screenshot etc) your pdf to Jpeg. It does not list pdf as an acceptable file type. (I assumed that the files were just getting too big.)
I never understood this. I arrived via Phuket on Dec 26th. Tested negative on arrival, but am now in BKK after 4 days. Am I just supposed to walk in to a specific place and say "test me for free"? People say they were given forms for their 2nd test, but the passengers on my flight were never given a form. 🤷🏾♂️