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The key to questions like this one is Avogadro's Number, which is the number of carbon atoms in 12g of carbon, or, say, the number of molecules in 18g of water. This number is roughly 6 x 10²³, (6 followed by 23 zeros, if you write it out longhand). One can use this to work through your aerosol droplet example. 18g of water has a volume of 18cm³ (because the density of water is 1 in these units). There are a million (10⁶) cm³ in a cubic metre, so this becomes 1.8 x 10⁻⁵ m³. Let's pretend your aerosol droplet is a cube rather than pear-shaped, as the error in doing this is not great and it makes the calculation simpler. A cube with a side of 10μ has a volume of (10⁻⁶)³ = 10⁻¹⁸ m³. So it will contain 10⁻¹⁸/1.8 x 10⁻⁵ ~ 5.5 x 10⁻¹⁴ of Avogadro's number of molecules, so the number of molecules will be 5.5 x 10⁻¹⁴ x 6 x 10²³ which is about 3.3 x 10¹⁰. This is 33 billion molecules. That's if I have not made any blunders in my arithmetic (which is easy to do with all these powers of ten, admittedly). Each molecule of water has 3 atoms in it: 2 of hydrogen and 1 of oxygen. So the number of atoms would be of the order of 100 billion. I'm not sure where your 1.3 million comes from but it looks far too small to to me. You can do similar exercises for other small volumes of other materials, but you need to know the molecular weight (molar mass) of the material and its density.

To some degree that is being done, but it takes a while to verify omicron cases as most cases need to be verified via sequencing, which has a significant delay (frequently around a week) before the data comes out. Edit: I should add that some producers of rapid tests have come out and said that their product will detect omicron, but I have not seen independent studies or results so far.

We had a briefing recently suggesting that lateral flow tests are likely not compromised, however as of last week I have not seen any larger scale data (the presented report was only on a handful of positive patients). I should add, that part of the careful optimism in that regard is because omicron only has few mutations in the nucleocapsid gene. Two seem to be specific to omicron (PI3L and Del31/33), so there is some effort to check out whether those could alter the results, whereas the two other commonly observed mutations were already found in alpha, for example.

Do you know of any solid evidence (yet) that confirms whether or not a lateral flow test does detect the new omicron variant ? That is does it produce a positive result even if it doesn't distinguish variants?