Attacking adjacent tile costs movement points if you use auto resolve. Fighting the combat manually does not cost movement points.

Exiting cities costs 0 MP because it is not considered movement, it is considered ejecting an unit from the city.

It seems to me that roads always cost 1/2 mp, regardless if you enter from a connecting-road square or not. Woods always cost either 2mp or whatever your remaining mps are (if you have .5 mp you can still enter a woods) except in the case of woods-road squares. hills and marsh are equivalent to open ground. Cities are wierd, it seems "free" to exit into the first adjacent square to a city (sprawl), and whatever normal cost beyond that, entering a city costs nothing either, but you need at least 1mp to enter the city or your movement ends adjacent to the city. I have not had a problem attacking any adjacent monster at no cost as long as you have at least .5mp. You never actually "move" into an attacked square, if you win the battle you have the option of moving into the now-empty square as normal.

I've never actually built a ship this game. I always play on large maps and it seems it's always one huge continent with a bunch of lakes, which I happen to like btw, so I have no idea what water movement is like.

Also, mountains are impassible, as are coastal hexes, but if you cast "raise" or "lower" land there seems to be a bug. I typically "lower" land on mountains because the mountains are usually too long, and sometimes the game lets me move on the, now ground-level ex-mtn, square but sometimes it doesn't. This is extremely irritating, as I find "lower" land one of the most useful spells in the game given that mountains always seem to be constructed in either very long chains or in a big circles .. and I've actually found AI kingdoms encircled with no way out and just one city. It seems their sovereign has never heard of the "lower land" spell  

I always use the cloth map board with grid, as it's much clearer what terrain is in what square.

EJCTING from a city????  HAHAHA what is it a falling airplane? This game need some serious fixing, the fact that they used squares instead than hexes is the first sign that their ideas weren't that clear!

Personally I can't stand hexes. Or wargames come to that

If you consider a grid based game map using squares and we assume three sort of layers of map info, units, terrain, movement, then we could represent each as follows,

Unit info:

[{0,0,0},{0,1,0},{0,0,0}] ---> a single unit standing in the middle of the map.

Terrain info:

[{1,1,1}, {1,0,1},{1,1,1}] --> all the terrain is of type one except the middle which is type 0

Movement info:

[{1,1,1},{1,0,5,1},{1,1,1}] --> The movement is 1 mp for all squares but the middle which is 0.5

In general, you would probably handle all these matrices as one matrix with each square holding the information for each of these layers.

Now, since each square can be assumed to have an inherent label of (i,j) denoting its place in the matrix, it is easy enough to denote adjacency by simply using the axiom that two squares are adjacent if they are 1 off from i or j ( we could make this 1 difference exclusive to i or j, to denote only 4 directions of moment).

If it did, then they did an amazing job making me believe that it didn't.

Good point. Certain wargames make you count that 1/2 bounus ONLY if you go from a road hex to another road hex (usually they are very large scale maps, since crossing from one hex to another represents several miles/kms and giving a road bonus would be particularly absurd if there is none for miles).

The problem here is that all seems illogical... auto fight uses MPs and manual battle do not? So I am forced to play easy, boring, useless battles otherwise I waste half of my movement? DO I HAVE TO BE BORED?

I even played wargames that tried to play on a grid made of octagons, of course that is not possible, so they alternated squares and octagons... weird... but interesting to try. According to where you were you would have 4 or 8 directions to take (Waterloo by International team - Austerlitz by the same brand, and they made Jena too I think...). Diagonally you would move from an octagon to another but sideways they had to insert squares.

Anyways with squares there is no way to apply penalties for movements since you would either be able to move diagonally or not. You would either lose 1MP or gain one when moving diagonally, but then again you could also alternate diagonal and 'parallel' movements...

Anyway my post is more about the logic of things like: I can enter a wood tile and spend all my movement or being able to first move in one plain square AND also by one wood tile and also spend all my movement, or doing certain movements and in certain situations also being able to attack, while in other apparently similar situations NOT being able to attack... I am not being more clear, sorry, because I just don't understand the system and have the feeling it is badly implemented... thus I was asking for an explanation.

Anyway making the first hex when walking OUT of a city cost 0 just feels wrong, especially because it only seem to cost zero if you do not stop in that hex, if you do it cost the regular amount of points that tile normally would. A real mess IMO unless someone can explain it!

It would still likely use a grid, but the grid would be too small for the player to notice. This would consume alot of memory and take tons of processing power to manage, so it is not likely to show up for a long time if ever.