Tricky
Briefly immortal
Geology is such a broad subject. It sounds like many of your questions relate to historical geology. This one is good, but very pricy. (Textbooks usually are.) You might also look at some sedimentology and stratigraphybooks or links if you're looking for depositional stuff. This link is a decent introduction.
For evaporites, you might try something on White Sands which is an active gypsum evaporite basin in the US. The Dead Sea and Great Salt Lake are saline evaporite lakes, actively depositing salt on their bottoms. The deposition is fast enough to be easily measurable.
Lithification of sedimentary rocks is indeed a continuous process. If you drill a well offshore, you grade from essentially muddy water to watery mud to solid mud and so on down until the "firmness" is enouth to consider it rock. Of course, you have to find a place with continuous deposition to do this.
But not all lithification happens at depth. Sometimes you get sands that are lithified near the surface as cement is deposited between the grains. This is called beach rock and it can be quite hard.
I'm not sure what you've heard about the formation of flint (which is just one of many kinds of cryptcrystalline quartz, or "chert") so I'm not sure what parts you find hard to believe. Remember though that lots rock processes occur under great heat and pressure which supersaturates the fluids with things you wouldn't normally consider soluble in water.
Yes, you can definitely see modern cross-bedding, not only on aeolean dunes, but even on beach and lake deposits, although they are smaller scale. In the field, one technique is to take a large pane of plexiglas with one sharpened edge and hammer it down into the dune, then scrape the sand off the side until you can see the "window" into the dune. They aren't as dramatic as ancient crossbeds because the boundaries in ancient beds are often enhanced by fluid movement through them. Also, differential erosion strongly highlights bedding planes. Still, modern cross-beds are easily detectible. They're one of the forms that you can actually study fairly quickly, because aeolean dunes form and migrate fairly rapidly unless held in place by vegetation. They may migrate many feet, or even miles in a single year.
I wish I could help you more, but these topics are wide-ranging. A lot of them might be answered by an introductory-level geology book. I haven't been to school in a long time, so mine are hopelessly out of date. Call your local university.
