No. When a map is created from a template, that map copies the current template settings. It has no connection back to the original template, and changing the template will not affect any maps created from it.

If you have added new things to a template you wish to bring into an existing map, you can make a new blank map from that template, then in your existing map, use Draw -> Insert file, pick the blank map you just created, but once you have it on the cursor ready to place, just hit escape instead of going through placing it. This is enough to copy in all definitions to the map, including symbol definitions, fill styles and line styles. Note that it doesn't update existing definitions, it just copies new ones.

Notice that if a fill is NOT scaled, your map is likely to not look as good when exporting to an image as it looks in CC3+, because the fills doesn't have a fixed scale, so they won't be the same size in the export as in the on-screen view (Typically, they will be smaller and thus tile more).

Also, if you don't set it as scaled, it won't stay the same size as you zoom in/out of the map while working either.

Are all the folders in the proper locations? Those blank entries in the latest screenshot of yours is typical indication of symbol catalogs not being where they are supposed to be. Basically, the config in CC3 says that a catalog should exist, but the actual catalog file is not found.

For example, that top catalog file in the screenshot is expected to be found at

@Symbols\Medieval Symbols\Artisan Buildings Wooden Shingle.FSC

(Remember that @ represents the location of your CC3+ data directory, so with a default CC3+ install, this would be c:\ProgramData\ProFantasy\CC3Plus\Symbols\Medieval Symbols\Artisan Buildings Wooden Shingle.FSC)

If there are any differences at all here (such as an extra folder in the middle or that path, or a missing folder) it indicates that things are not where they are supposed to be, and something has gone wrong at some point.

If you insert an fcw file into another using Draw -> Insert File, the line styles (along with fill styles and symbol definitions) will be copied over. Basically same trick as for copying over missing fill styles.

The filters those buttons use are set up to be compatible with the standard CD3 style cities. When used with other styles, they simply doesn't find the correct master filter, and ends up displaying the default set of symbols from whatever style your map is in.

You can toggle the filters used by using the :CC2SYMPATH: button. Each click switches to the next style in the list, or you can right click the button, pick master filter settings, and pick the desired one (These buttons want the CD3 Bitmap A one). Some styles may not have the right option in the list however, so another way of doing it is to click the :CD2: button once.

Note that changing symbol style will affect all other symbol buttons too though. The easiest way to get back to where it should be for your maps if you can't seem to do so using :CC2SYMPATH: is to simply save your map, then go to the File menu, and pick your just saved map from the top of the recent file list. This reloads the map, including restoring the default settings for that map.