1) Could the dust/sand/insects from the air have made its way into the oil via the dipstick hole and cause damage?
I wouldn't say absolutely nothing made it's way into your engine via this route, but the dipstick tube is so small (relatively) and the amount of oil which can be on the dipstick is so small when you pull it out, even if some dust/sand/insects got caught in/on any part of this, it would amount to nearly nothing.
2) Could the dust/sand from a dirty rag cling onto the dipstick and get in the oil and cause damage?
When you wipe of the oil, any dust/sand on the rag won't transfer to the dipstick unless you've got some serious crap on there. Easiest way to avoid it is to just shake out the rag. A couple of few good snaps with your towel/rag will get any dust/sand off of it and it will be ready for use. Anything else which may be on the rag won't transfer to the dipstick because it will be trapped by the rag itself.
3) Would the oil filter be robust enough to catch this small amount of grit?
Oil filters typically try to filter down to the 6-10 micron range. When a filter gets down to the 3 micron range, they start removing additives in the oil. Ultrafine dust particles refers to dust which is about 2.5 micrometers in diameter, nearly a 30th the thickness of human hair. The thing is, when dust is this fine, it remains suspended in the oil and doesn't cause any issues to the engine. Would a bunch of it cause issues? Absolutely, but the amount you are talking about isn't going to do much at all. The saving grace may be, if the grit is in the oil for any appreciable amount of time, cleaning agents will cling to it, causing it to be bigger in size, which will allow it to be trapped by the filter.
4) Is the movement of oil as such: sump (what dipstick measures) -> filter -> pump -> camshaft?
It depends on the oiling system, but usually it goes from sump -> pump -> filter -> rest of the engine. Some engines pump it to the camshaft and then down to the crankshaft. Other engines have what is called priority main oiling, which sends it to the crankshaft first, then out to the rest of the engine.
5) What type of damage occurs from grit in the oil?
If enough grit which is not caught by the filter is in the engine, it can cause wear on the internal parts, including the crank & cam journals, bearings for each, cam lobes, cylinder walls, etc. Pretty much anywhere there are wear surfaces.