Is the Scrum Master responsible for resolving all the issues of the Scrum Team?

Personally I would say the answer is "No". The Scrum Master is responsible for helping the team unblock/resolve any impediments. This is different to "resolving all the issues". The team should eventually be able to resolve many of the issues they encounter themselves.

But I may be wrong - interested to see what others think.

I'd have selected false as well.

I have a concern with the word "responsible" instead of "accountable". But even making that change, and saying that the Scrum Master is accountable for resolving all of the issues of the Scrum Team, still doesn't make the statement correct. The Scrum Master's obligation is to help the team and organization to be able to identify and remove impediments. There may be things that make sense for the Scrum Master to "just do", but the team and the organization needs to be involved, to various degrees, to make sure that issues are resolved in a way that is appropriate to enable the team or organization to maximize productivity.

would it be right to say the Scrum Master may also remove impediments affecting the whole Scrum Team?

The Scrum Master may remove impediments to agile practice which affect the whole organization, but only if people want them to be removed.

I would suggest that the Scrum Master may be held accountable for ensuring the transparency of impediments, regardless of whether or not people wish to see them.

A lot of third party websites do not represent the best of scrum knowledge and full with flawed information. 

I would too have chosen 'false', given the scrum teams are self-directed and organized they are empowered to resolve conflicts within team. Team would ask scrum master's help if there is an impediment or an issue outside scope and power of the team.

Also, scrum master should have keen eyes on scrum practices and values being realized by day to day behavior of the team and make any such issue transparent.

I agree with false. IMO the scrum master should coach the team to help them understand how to remove their own impediments, empowering them? If the team isn't that mature though, I agree the scrum master should do this initially.

...resolving all the issues of the Scrum Team

The use of the word "issues" is throwing me off a bit. Do they mean impediments to producing the Sprint increment or problems the team is having that affects their ability to work as a team?  The question is really ambiguous. 

But even given that confusion, I say FALSE.  From the scrum guide:

The Scrum Master is responsible for promoting and supporting Scrum as defined in the Scrum Guide. Scrum Masters do this by helping everyone understand Scrum theory, practices, rules, and values.

That says nothing about "resolving all the issues".  Yes the guide goes on to elaborate on things for which the Scrum Master is accountable for the Product Owner, Development Team and Organization.  But even those items listed say "in several ways, including".  That tells me this is not a definitive list and leaves a lot open to inspection and adaption. 

If a Scrum Master was responsible for resolving all of the issues of the Scrum Team what is left for the rest of the Scrum Team to do? Isn't a Product Backlog Item an issue that the team needs to resolve? If I, as Scrum Master, am responsible for resolving all of the Product Backlog Items why would I need Product Owners and Developers?

As the question in your last paragraph go back and read this from the beginning because I would say the same thing if you asked it in a different post.  :) 

As usual I have a different perspective but I'm okay with that. You be you, I'll be me.

My thoughts --

• A Scrum Master should NOT be responsible for solving ALL the issues of the Scrum Team. They should facilitate the resolution of issues and/or take on anything that would be of help to the Scrum Team (this is subjective). For example, if a Dev Team member came to me complaining about another Dev Team member, the very first thing I would ask is, "Did you speak with them or provide them this feedback?". If not, I would say, "You need to go talk to them immediately, and if you are not comfortable, I am more than happy to assist you in this conversation." I would not solve this for them as it could harm the empowerment of the Scrum Team by painting me in an authoritative light, which a Scrum Master is not.
• As well, in my experience, a Scrum Master more often than not, cannot remove impediments directly but can facilitate/lead/focus the attention of the removal of impediments. Of course, there are times when the impediment can be removed directly by the Scrum Master.
• The goal should be to empower the team to be self-organizing and self-managing. Overstepping the Scrum Master's role scope can impede this progress or create a sense of "Project Manager" aura around the Scrum Master and create resentment around Scrum.

Although, SM don't have responsible to resolve all issues impact to Scrum Team, however, SM should follow and consult to resolve or update result for issues which  beyond the abilities of the Scrum Team.

This is the best way to SM get more values with his team. Simple: SM is member of team, we are a team.