In ElementalDefs.XML, found in FE Legendary Heroes\data\english, there are several "MinDistancesBetweenCities" settings (each applies to a different map size) that you can adjust that will force cities to be more spread out, and therefore cities will be less numerous. Note that fewer cities means less income and less research, which tends to make for smaller armies of less powerful troops, though how the AI will handle this I could not say for certain.

You could also find the "MinTotalTileYield" entry in the same file and increase that number, which will on average reduce the number of available settlement locations, though these locations will generally be better locations. Note that you should not increase this too far or you may not have any possible settlement locations available on the map. Alternatively, you could find the "MaxTotalTileYield" entry and reduce that, though I'm not sure if that will just make the settlement locations which exceed the maximum yield worse or if it will prevent those tiles from showing up. Also note that increasing the "MaxTotalTileYield" entry doesn't normally do much unless you also change the values used in the yield calculations, as generally speaking you will not have a total yield much higher than 9 on any given tile using the default game numbers. If you wanted to change tile yields, you'd have to dig around in CoreWorldResources.XML and TerrainTypes.XML, and perhaps a few other files, looking for where the tile yield properties are set and changing those to your tastes.

If you are familiar with the map editor included in the game, you could also create for yourself a map with a more limited number of settlement locations.

Not as long as the border of the outpost contains the area. However, nearby cities, or in older versions newer outposts, can change where the line is drawn, which can allow settlement in locations which were formerly safely within your borders. Note that it is legal for a pioneer to settle in any little gap in your borders, or establish an outpost in such a location, which can affect where your borders lie.

1) You can't settle someone else's territory. You can actually incorporate this into your strategy by blocking the AI from settling in areas by using outpost or arcane monolith spam.

2) You could try smaller maps to limit the amount of cities around. Or focus on winning through the non-conquest routes so that the AI city spam becomes less of a relevant issue. Tweaking the difficulty upward is also probably a good idea as a more challenging experience will help keep you engaged. Or you could try making a completely under-powered sovereign with abilities suitable for strategies you normally don't use and have the satisfaction of taking him to victory despite his or her flaws.