Few clarifications required

1.   This is from the Scrum Guide section that explains the Scrum Master role.

The Scrum Master serves the organization in several ways, including:

• Leading, training, and coaching the organization in its Scrum adoption;

• Planning and advising Scrum implementations within the organization;

• Helping employees and stakeholders understand and enact an empirical approach for complex work; and,

• Removing barriers between stakeholders and Scrum Teams.

What do you think the answer to your question would be?

2. No one assigns work in a Scrum Team.  The Scrum Team is self-managing, self-organizing.  The Developers will organize their work with the intention of satisfying the Sprint Goal.  The purpose of the Daily Scrum is for this organization.  

3. The Scrum framework is based upon self-managing, self-organizing teams in order to produce value.  There is nothing said about performance reviews, hiring/firing, etc.  So any answer to that question falls outside of the boundaries of the Scrum Framework.  We would all like to think that situation never occurs, but we know it does.  We also know that there are very few organizations in the world that don't follow the old style military like hierarchy of roles and management levels. So in reality, the hope is that the organization will be able to understand the way to integrate the empirical methods of Scrum into an organization without introducing the overhead and burden of the command-control that so many companies have.

4. This statement is in the Scrum Guide section that explains the Product Owner role.

The Product Owner may do the above work or may delegate the responsibility to others. Regardless, the Product Owner remains accountable.

You asked if the Scrum Master can suggest.  In reality it is the Product Owner that should be asking for the input.

5. Not sure what an ST is but every theory I have ever read about change says that when change occurs, productivity will be impacted.  It may be positive or negative impact but there will be impact to change.

Does SM helps people outside the team interact with Scrum team?

Yes. The Scrum Guide calls this out in a few places when describing the accountabilities of the Scrum Master. One way that the Scrum Master serves the Product Owner is by "facilitating stakeholder collaboration as requested or needed". This includes, but isn't limited to, the Sprint Review. There are also services provided to the organization, including "removing barriers between stakeholders and Scrum Teams".

In any scenario does SM assign tasks to development team when they need work?

This would be antithetical to the Scrum Master's accountability of coaching the team in self-management. A self-managing team doesn't need someone to assign work to people. They should be able to effectively plan and pull work as needed.

Who is responsible to remove a developer who is creating hostile environment? I hear answers like Scrum Manager .Is it correct as there is no such role in Scrum

This is more dependent on the organizational structures that exist outside of Scrum. The Scrum Master would be involved in this, such as by coaching the team in self-management, helping to remove impediments, and removing barriers. If the team believes that an individual is creating a hostile environment, the team should be empowered to raise these concerns to the person or people in the organization who can remove the problem. Removing the problem may not necessarily be removing the person from the team but giving them the training and information about the effects of their behavior and an opportunity to self-correct.

At times when PO is struggling with ordering the backlog, can SM suggest that Development team do the ordering to check the feasibility of work?

The Scrum Master suggesting this could be a fine line between the Scrum Master taking a managerial role for the team and the Scrum Master serving both the Product Owner and the Developers. The Scrum Master handles helping the Product Owner to effectively define the Product Goal and manage the Product Backlog. The Scrum Master is also responsible for helping the whole team to remove impediments and create high-value increments. Personally, I believe that what to do comes down to how impactful the problem is. My preference would be to let the Product Owner and/or Developers see and raise this as a concern on their own, but the Scrum Master also has some responsibilities to the stakeholders and the organization to not just let the team fail.

Will there be any impact on the productivity when new STs are added ?

Probably. An organization is a complex system. Changing aspects of a complex system may have some effects on other aspects. But it's hard to say what those effects would be. It also depends on the method by which the new Scrum Teams are introduced to the organization and the product.

If I can improvise my questions, I think I can get to know more.

That isn't what you've done. You've prescribed a narrow range of answers. None of the available options are very good, and making a false choice is unlikely to improve understanding. 

1. Maybe the developer does not need "removing" at all. Instead, perhaps there is a need for a self managing Scrum Team to take action.

2. Either could be of relevance, depending upon why the Product Owner is struggling.

3. Any or no impact on productivity is possible. Whether productivity increases or decreases may depend on the period of time over which it is measured.

Had I known that I was helping to create quiz questions, I probably would have answered quite differently.  Your new suggestions are still not correct.  Truth is that there is no "appropriate" answer to any of your questions.  Every time that any of those situations arise, they should be evaluated independently of any previous incidents.  The only correct answer is what is correct for the specific situation. 

As both @Ian and @Thomas have pointed out, there is much more to consider about each situation.  Empiricism is the key.  Each time you encounter a situation, inspect it and learn from it.  If you are encountering the same problem over and over, do you really think that doing the same actions will result in anything different?