Slitherine

As shown on attached screenshot, attack path of my cavalry is quite strange - if I clicked the attack button, the unit would have enough APs to make two sharp turns (something that is not normally possible): turn 45 degrees to the right, and then 45 degrees to the left and then charge the irregular foot. But if I only moved it directly to the right square it wouldn't have any more points to continue the advance.

Perhaps it is so, because the game doesn't take the patch of rough ground there into consideration, when suggesting attack options in this particular situation?

Another question: why can't I charge the slingers, if I can charge both the clibanarii and the other (disrupted) cavalry unit?

In this case I think the unit only considers the path it has chosen because it would default to choosing a path avoiding the rough terrain if possible. The game (for good reasons which I won't go into here) only considers the overall change in direction from the start position to the end position of a move/charge. This does sometimes lead to odd situations like this.

So to summarise, the unit has tested a route to the infantry avoiding the rough terrain (or possibly just avoiding the unit on it). Ignoring intermediate turns, the overall move is within 45 degrees of straight ahead, and the AP required is therefore 12, so the charge is permitted.

It can't charge the slingers because once it enters the square in front of it, it is ZOCed by the two cavalry units, but not by the slingers because they are light troops.