-Do commissars have ranks inside the organization of the imperial guards?
-Can a commissar give commands to officers?
-What is the relation between the commissar and party's support specialist players? Like psykers and tech priest assigned to a squad.
Or he has authority only in "Morale" and "Political" matters? If so, what kind of matters are considered to be as such?
None of the following is official: it is merely my own personal take on the subject.
A Commissar is an agent of the Departmento Munitorum, which is in turn the Department of the Adeptus Administratum responsible for the raising, supply, maintenance and deployment of the armed forces of the Imperium. It is his responsibility, on behalf of the Departmento Munitorum, to personally ensure that the Emperor's armies are operating in the desired manner, as defined by military law.
Commissars possess no rank within the Imperial Guard (or Imperial Navy, for that matter - Naval vessels have Commissars too) - from an organisational standpoint, they are advisory personnel attached at the regimental level.
Commissars have no inherent authority to issue orders to anyone. When it comes to other advisory personnel (Tech-Priests, Preachers, Sanctioned Psykers, who hail from other organisations), their oversight extends only to military matters. Storm Troopers, Ogryns, Ratlings and other cross-attached specialists are still Imperial Guardsmen of a sort, so they are covered by a Commissar's duties.
It is the unending responsibility of a Commissar to ensure that the forces under his authority (the regiment or vessel to which he is attached) act in all ways and at all times in a manner befitting a sworn servant of Him on Terra. This begins with upholding the laws and regulations that govern the military (if you are in breach of regulations, it is a Commissar who will oversee your interrogation, judgement and punishment, though he is not necessarily the one who will administer such things), and ends with ensuring that the officers bear the responsibilities of command with sufficient piety, courage and solemnity (that is, that an officer is not misusing Imperial forces, is not a coward or traitor, and is issuing orders that serve well the needs of the Imperium). For a trooper, the Commissar is the man who ensures that you are punished if you do something wrong. For an officer, he's the one who ensures that you don't get the chance to do something wrong. In either case, while a Commissar cannot give orders, he is nonetheless someone who must be listened to, especially as part of his job is passing approval over the orders of officers.
In the field of battle, a Commissar's responsibilities do not cease - it is his duty to ensure that everyone fights to the best of their ability, whatever their particular role. It is here that the Commissar is permitted to judge and punish any infractions he witnesses instantly and summarily, though the range of infractions that must be punished immediately (as opposed to ones dealt with post-battle) is relatively small and covers things like cowardice, desertion, surrender and so forth - things for which the punishment can only be death.