What's the actual purpose of those functions? When do they have to be used? I met them many times (and used couple of times by intuition), they are usually called when moving an object by a long distance (teleporting), however they do not seem to be called when actor's self movement is calculated.

They must be called when actors position (x and y) is changed. They are used to update actor's links in blockmap which will update actor's Subsector and Sector fields.

Is it necessary to Unlink actor before his Origin will change, or one may only call LinkToWorld after it was changed?

LinkToWorld will unlink it if it's still linked.