Thanks to those who played! Examples 1, 3, and 5 are the struck counterfeits, all in genuine TPG holders.
The reverse die that was used for the 1806 No Stems Half Cent (Cohen Variety #1) was one tough customer. It was used to make the 1804 Crosslet 4 Stemless (fairly common), 1804 Plain 4 Stemless (the most common half cent in my opinion), 1805 Small 5 Stemless (the most common 1805 variety) and the 1806 Small 6 Stemless (the most common 1806 half cent). It's hard to estimate how many coins it did make, but it had to be in the 10s of thousands. Example #2 in the OP is deceptive because the die was on its last legs by then. It was getting very tired and it was rusted. That coin would be a hard one to authenticate if you were told that some them are bad. Plus it also has some green on it which looks like the stuff the Chinese use to "age" their junky products.
The best estimate is that the stemless reverse struck about a million coins over the three years it was in use, far more than any other half cent die. The "average" Draped Bust die struck less than 200K coins, but the variance is so large that the notion of "average die life" for the series is meaningless.
A million sounds a little high. Here are the mintages for the 1804, 1805 and 1806 half cents with the number of die varieties. 1804 1,055,312, spread over 12 die varieties with two of the most common using the Stemless reverse. 1805 814,464, spread over 4 die varieties. The Stemless one is the most common, but the large 5 Stems is also fairly common. The Small coins are scarce to rare. 1806 356,000, spread over 4 die varieties, The Stemless one is the most common, but the Large 6 stems is fairly common. The two Small 6 stems varieties are very scarce and rare. With a combined mintage of 2,225,776 for the three years, I don't think that half of those coins were the stemless pieces, given the common nature of coins like the Spiked Chin and the more common 1805 and 1806 varieties. Certainly 800,000 could be possible, but 1 million might be a stretch.
Those values are from mint reports. They do not reflect the numbers of coins with those dates. 1804 and 1806 are more common than those numbers would suggest. 1805s, however, are far less common. The 1805 without stems barely makes R1, and it is easily the most common of the date. You can look it up. I addressed the apparent mintages of each of the Draped Bust dies on page 86 in my book and the probable actual mintages of coins bearing each date on page. 84.