Sometimes i get very strange result when printing which is not desirable as it ruins whole project, here are some photos of it, what may be the cause of that? I use ABS with heated bed and glass with glue as bed

Looks like you are starting the print on top of the support structure. That typically does not work the best because for the supports to be easily removable you need a small gap such as 0.3mm or so. So when the print starts its starting in the air and never gets a good solid base.

or did the support structure move from where it should be? Hard to tell which issue this is with only pictures and no real info on what happened. If the support moved try adding a disc to bottom of print and then supports on top of that so you have a large surface to the print bed. Simplify3d lets you do this already by choosing how many base layers before support.

Agreed, this looks like a bed adhesion issue. A raft or more dense infill, with dense infill layers before the model, may help. Increased bed adhesion is a good idea too.

I suppose the part on right moved a bit but I dont really know why it moved as the adhesion was perfect I can say, it is like it got moved by the nozzle or something as why would it unstick when also the part unsticked was stragiht (there was no warping so no typicall unsticking)