Project Plan/ estimation

I am in a project where PO is assigning task to other such as me as SM or Agile analyst?

Going to start with why gives the PO the authority to assign work?  I can see them asking for help but in Scrum, assigning work is usually a problem. 

who is responsible for project monitoring toward road map/ release plan?

Responsible for and doing the work are two different things. I would say that the entire Scrum Team is responsible for monitoring progress. It should be apparent based on the value that is being delivered. Search the Scrum Guide for the word "progress" and notice that it is usually generalized in context of the Scrum Team.  I will point out that there is a subsection in the Product Backlog specifically addressing this topic.  Here is a cut/paste of that section.

Monitoring Progress Toward Goals

At any point in time, the total work remaining to reach a goal can be summed. The Product Owner tracks this total work remaining at least every Sprint Review. The Product Owner compares this amount with work remaining at previous Sprint Reviews to assess progress toward completing projected work by the desired time for the goal. This information is made transparent to all stakeholders.

Various projective practices upon trending have been used to forecast progress, like burn-downs, burn-ups, or cumulative flows. These have proven useful. However, these do not replace the importance of empiricism. In complex environments, what will happen is unknown. Only what has already happened may be used for forward-looking decision-making.

Yes, the Product Owner tracks the information and that information is made transparent to all stakeholders. All of the information used is provided by the past activities of the Scrum Team.  So in my mind the responsibility extends to the rest of the Scrum Team.  The Product Owner is ultimately responsible the activity of projecting, presenting and explaining the progress but the burden lies on everyone to contribute to the activities. 

I'm going to take a slightly different take than Daniel Wilhite.

The Scrum Guide defines the work of "Product Backlog management". Two of the items included in Product Backlog management are "optimizing the value of the work the Development Team performs" and "ensuring that the Product Backlog is visible, transparent, and clear to all, and shows what the Scrum Team will work on next". I'd argue that forecasting or planning actual releases and communicating this to stakeholders falls squarely onto the Product Owner.

However, the Scrum Guide also says that the "Product Owner may do the above work, or have the Development Team do it". Even in this case, "the Product Owner remains accountable". Some work or decisions may be delegated to the Development Team, but I would expect collaboration with the Product Owner so that the Product Owner is able to remain accountable.

I would agree, though, that assigning work is problematic. Scrum Teams are self-organizing. The Product Owner (or the Scrum Master or one or more members of the Development Team) should be assigning work to others. It should be a collaborative effort to understand the work and help each other as needed or requested.

PO is responsible for vision road

What if the PO does not have enough time for managing the progress towards the vision thing? What would a good Scrum Team do in this situation?

Filip, I guess a good scrum team would live in an atmosphere of respect, openness and transparency. As such, the PO would openly voice his concerns to the team to make sure the others know that he is facing a problem in optimizing the value delivered by the Development Team, and the team can discuss ways to help/enable the product owner with his responsibilities and accountabilities.

many thanks to you all :)