End to End plan for Agile coach

a) As an agile coach what will be your end to end plan for changing mindset of team from Waterfall to Agile

I would respond that there is no such thing as an end-to-end plan for this because every team learns differently and at different paces so I would be creating the plan as I go based upon current knowledge.  In that manner I would be educating the team on how agility works and how to do accomplish the "do something, inspect it, learn, adapt as necessary" loop works.

b) While doing estimation, why should we use Fibonacci series, why not simple numbers like 1,2,3,4 and so on

The modified Fibonacci series was originally used because it progressively gets larger.  What is the real difference between a 4 and a 5 in the simple number series?  In the Fibonacci series, it is easier to understand the differences because the gap between the numbers get larger.  A difference between a 5 and an 8 is easier to understand than between a 5 and a 6. 

You also need to point out that estimation using a Fibonacci sequence is best when using relative sizing.  Is this effort more than other efforts that are estimated as a 5?  Then it would be an 8.  This doesn't mean that it will take 8 hours while the others take 5 hours.  It just means the 8 is bigger than the 5 but smaller than the 13.

But in the end, it all depends on what the team doing the estimation feels is the best method for them.  As I said before, every team is different.  So a 5 for Team A might not be the same as a 5 for Team B, no matter what scale you are using. 

a) As an agile coach what will be your end to end plan for changing mindset of team from Waterfall to Agile

"Interesting question. Help me to understand the timescales for that plan, and where the sense of urgency for any change at all will come from."

b) While doing estimation, why should we use Fibonacci series, why not simple numbers like 1,2,3,4 and so on

"Simplicity is good. Try it! Find out how well that simple scheme works out for you when deciding if something's a 10 or an 11."

a) As an agile coach what will be your end to end plan for changing mindset of team from Waterfall to Agile

Whilst considering the ethical questions around whether it is my 'right' to change their mindset, I would simply take the first step and see where it leads. Take the problem to the team, identify what they need, and work with the organisation to provide it. Simple.

b) While doing estimation, why should we use Fibonacci series, why not simple numbers like 1,2,3,4 and so on

Rather than considering the purpose of estimation as sizing work (that's still valid FYI) try changing viewpoint to simply gaining transparency and creating conversation. My general response, whenever I get asked this question, is to say 'I don't care if you size things using numbers, animals or computer models. As long as you are clear on their relative complexity and can help the Product Owner order the Product Backlog appropriately, crack on'.

I agree with Ian's point above though. Psychologically splitting a 5 and a 6 vs. a 5 and an 8 is easier. Our brains work in interesting ways.

a) As an agile coach what will be your end to end plan for changing mindset of team from Waterfall to Agile

An end-to-end plan for a complex task as a team's transformation would fit with how agile faces these situations? Are we respecting the first value of the agile manifesto (individuals and iterations over processes and tools) if we decide an end-to-end plan beforehand?  Wouldn't it be more proper to perform a team's transformation through an empirical approach based on continuous transparency, inspection and adaptation?

I totally agree with Gonzalo and Ryan.