My general understanding is that merchants have 30 days from payment to ship. The credit card billing or bank statement will show the date the purchase price was charged to your account, and that would be the best guide to determine date of payment.
I wait until after the 30th day after payment before requesting the status of the order, and I think merchants appreciate that. If no prompt reply, and no other reason for delay has been communicated by the merchant, I would have no qualms about a complaint with the US Federal Trade Commission. Also, the Attorney General of the merchant’s home state may have a consumer protection bureau which would be of assistance. State attorney general information is available online.
Although some states have consumer protection laws that include provisions for treble damages for unfair and deceptive acts and practices in trade or commerce, your residence outside the USA would probably make a small claims action pointless, unless you travel regularly to the USA.
In my experience, products are delivered here within or close to the above described 30 day period; however there a few that have not been. But I’ve always received responses to inquiries for status after the 30 days, and have never had to take legal action as described above.
Also, most online merchants warn customers up front of delays due to the pandemic. But I have no knowledge of the legal effect of these warnings on the above 30 day rule. If you were to contact a state’s consumer protection bureau, though; you would probably find out more about this.
I agree that stonewalling your inquiries is rude in the extreme, even though the merchant may be within the shipping period. I inquired about an order from another merchant well known to BPL members because I did not receive even an order confirmation by email as you did, although the charge was made to my credit card. Finally got someone on the phone who claimed that not only was an order confirmation emailed, but responses to my inquiries were emailed as well. Like your inquiries, my emails were earlier than the 30 days, in my case because I did not receive even an order confirmation. In any event, I was assured the order would be filled promptly, and it was.
If you want the tent, as opposed to a refund, then suggest waiting until 30 days from the charge before taking further action; but note that some credit cards require notice to the issuer within a specified time from the charge should you be seeking a refund. If the transaction was through PayPal, there are additional remedies that I understand are consumer friendly.
With the pandemic, I’ve experienced these kinds of difficulties even more than before. I think your post will be appreciated if for no other reason than alerting us to the perils of overseas ordering during the pandemic. Thank you for reminding us how important trust and responsiveness are to consumers.
Please also note that I am not a merchant, nor affiliated with one.