Is there any way to set the position of pushpins/shapes in the map in a way that the pushpin/shape cannot be dragged/moved or similar? In another words, is there any way to do not let the pushpin/shape be moved and make his position be unalterable?
Thanks in advance

Interactively using Mappoint, probably not. Programmatically I think it is possible. One appproach might be to check the location of the object(s) in the "MouseUp event" or some other event and see if they do not exist anymore or the location does not match, if so put them back where they belong.

There are several ways to get the job done I'm sure...

If you just wanted some guaranteed locations you could import a table of locations each time. As long as you import( and the database remains unchanged) you will be guaranteed those locations not to change. I admit it is a very low tech solution, but if it helps ;)