I think this is a deliberate artistic choice in this style, but you can change it by "cheating" a little. The origin of the fill is determined by the lower left extent of the fill, so if you make a little notch somewhere that forces the start of the fill half a grid square down and to the left, you get your desired result. This little notch can then be covered up by the outside wall details:

As for the second question, you add grids to your map using the Hex or Square Overlay command found in the Draw menu.

Also make sure you have a proper hex snap grid selected (Right click the Grid button in the lower right). Having the right hex grid snapping active is what triggers the automatic resizing to fit the grid. Not that if you had a symbol on your cursor when setting the snap grid, you need to pick up a new symbol from the symbol catalog to trigger the sizing.

Most templates have references for these available as part of the template.

Hit the :ICON_DRAWING: button, and you'll most probably have them available near the top of the symbol catalog window.

I'd say that's up to you.

My general "rule" for the atlas is that if you map a feature, it needs an appropriate symbol on the parent map to be linked from, no placing something in an empty spot on the map just because it could conceivably be there. If no such symbol exist, an appropriate intermediate overland map needs to be made. Same for a map of a single place inside a settlement, a floorplan map shouldn't be linked directly from a city symbol on an overland map.

However, in this case, there is already a tower symbol on the overland map, so I have no issues linking your tower directly to this one. But if you want to make intermediate maps, be it overland and/or settlement that is great. After all, there is no rule to say there can't be a settlement around a tower, a symbol is often used to show the most prominent feature of the place after all.

AA in itself can't really be the issue. All turning on AA does is making CC3+ export a slightly larger image than requested, so the imagemagick processing after export can generate AA by reducing it down to the requested size.

Now, what I did notice is that when I export at 5000x5000, it is completed in a single pass, but if I bump it to 33% antialias, the resulting size increase leads to a 2-pass operation. Is that what you see as well?

My suspicion is that something weird is happening with the color key with that gigantic entity, but in this case, because turning on antialias forced it to become two-pass, it became divided over two smaller ones instead which was then handled correctly.