Both of my D&D groups allow you to move 1 square at a time (mini-moves). In most cases, the character moves from origin to destination without interruption, so the action appears to occur as a single event.
New information based on moving into a specific square is delivered as an immediate interrupt and the rest of the move action continues to be take 1 square at a time. So if objects appear or events occur due to turning a corner, shedding light X squares away, etc. then the character is stopped at the square in which the new information becomes available, the DM describes the objects or springs the events, and the character may then proceed based on the new information, 1 square at a time.
Kind of like chess, a character does not actually move until his hand is off the piece (figurine mini) and the action has been declared as final. During the move process, the DM or other players may optionally remind a player that they could potentially be drawing an OA if they pass a particular object. Either way, once the move is declared, the DM pauses a moment to let the player enact last-minute take-backs, then the OA is announced and the move cannot be taken back.
If there is a monster with possible threatening reach, the monster description never really suffices. In my groups, a monster knowledge check is allowed as a free action so you perform your check and do or do not know that the monster has threatening reach. If you don't know and get hit by it, that's the way it goes ... now you know.
"If an opportunity action pushes or slides a character, this should cancel the character's original move action, yes / no and why ?"
My groups play that it does not cancel the original move action (for the reasons stated in previous posts).
For the sake of discussion, ignore reality, since reality has no part in D&D actions. This is all about game balance. How balanced is it that an interrupt that forces movement steal my move action? If I am allowed to move 6, and an interrupt allows a monster to push me 1 square, does it seem fair that I lose the other 5 squares of my move? Is that balanced?