is diagonal distance of a tile 1.4 times of the horizonal/vertical distance or same with it? So, will going diagonal direction take more time than going horizonal/vertical direction each turn?
Conceptually, each move is 1 "effort", so rather than going 1 tile north and then 1 tile east, it is better to go 1 tile northeast directly.
Edit: I forgot to mention that, the terrain does matter. For example, if you have rock tile(s) in front of you, going around might be quicker/less tiring and possibly even safer, as climb action involves a risk.
Not something you asked here, but since you seem to have an efficiency interest, I will mention this one too, just as a FYI. When facing a direction, and wishing to face the opposite direction (i.e.: needing a 180-degree turn), you can do that via 4x 45-degree turns, 2x 90-degree turns, or 1x 180-degree turn.
These 45-, 90-, and 180-degree turn actions all have separate key bindings via left and right.
To see these, and many other key bindings, in game, press ? key to bring up the built-in help screen and checkout the MOVEMENT section at the very top.