Does this page help, Jim?

https://www.omnicalculator.com/math/hexagon

While Julian and Monsen are both right, and you are discussing function and scale, there is also an artistic aspect of getting the right Level of Detail (LOD) in a map.

Even in this day of technology some things are still better if they are judged by eye. Create your map to the correct CC3 scale for the area you are mapping (map units are miles or kilometers in an overland map, and feet or metres in city and dungeon maps), and paste a handful of the symbols you intend to use in that space at the default scale set by CC3 at the creation of the map (not too many - don't go overboard and start the map just yet), then render the mostly empty test map to the final size and examine it at 100% zoom, or print it the size it will be published at if you can at home - no need to get professional prints just yet.

Judge how much larger or smaller you want everything to be so that you have enough room to show the information you want in the map, and to be able to enjoy the symbols themselves - even though each mountain or tree may end up representing several mountains or trees due to their size relative to the scale of the map.

I don't recommend using different scales for different types of symbols in the same style unless, as Monsen points out, the settlements are a bit on the small side and not easy to identify. Pick a scale for the whole set and stick to it unless you have a rare exception (such as a world tree). Once you know what the symbol scale should be, set the default symbol scale in the Drawing Presets dialog |CC2PRESETS| and save the map.

Do two more tests like this to see:

• How thick your lines for coast and river should be, and how much detail you really need to draw in those two things. You would be surprised how messy a really accurate coastline with tens of thousands of nodes can look when printed on a piece of A4. Most maps have grossly simplified coastlines to avoid that mess and look so much better for it.
• Set the right font and size for your labels. Labels don't need to be huge (unless you are naming a continent, in which case they would probably be quite transparent as well to allow more regular town names to show through those enormous continent labels). But they must be readable without squinting.

It's worth the time and trouble to run a few quick tests first than to spend hours, days or possibly weeks making a fantastically beautiful map only to realise that it is a meaningless unreadable jumble when rendered to production size.

When you install the update you will probably get a message that tells you you have a newer version installed. If you do, just ignore it and carry on installing the update.

Most of the things you are highlighting as being an issue are down to sheet effects. If you put an Edge Fade, Inner sheet effect on the snow you will be able to show the bevel on the coast. You can also use one of 3 colour modifying sheet effects on the swamp areas to change the colour. These are (in order of ease of use) the Adjust Hue/Saturation, Colorize, and RGB Matrix Process.

I recommend using all the same mountains and hills if you are going to use a different style. the hills really don't look that bad, even if they are paler. In fact it is better that they are paler than darker than the land since it makes them look like bumps rather than hollows. You can always replace them later using Replace in the Symbol Manager if you still don't like them.

Sheet effects are always a personal taste. You can learn a lot by experimentation.

Looks great :)

The grass patches should be the same scale as the grass fill as long as they are set to the default symbol scale of 1. I have noticed that there are points as you zoom in and out of maps with a mixture of fill and patch that the patches sometimes 'click' to the next resolution slightly before the fill does. This shouldn't be a problem when exporting as all will be exported at the same resolution, but it can look like the patches are wrong in the CC3 window at certain zoom levels.

The other possible mismatch is if you are using the fill from one style and the patches from the other style. Creepy Crypts grass does not exactly match Forest Trail patches, and same vice versa. I personally prefer the Forest Trail grass texture and patches, but it's down to personal taste in the end.