Under which specific circumstances may Gardaí break the rules of the road?

I wouldn't have thought that we did. Is there any data to back this up?

That said, I frequently see guards driving while using a mobile phone. I don't think there is any reason for them to be on their phones while driving.

You're picking anecdotes/examples, familiar to you as an Irish person, but unless you're familiar with police services in France, Germany etc..I don't know how you can say we're the "most corrupt in Western Europe".

Is there any research/data to support your stance. There may very well be! But I would be very surprised if your assertion is true.

While there is a general exemption, there are some specific qualifications to that exemption:

• Not under the influence of alcohol (and can demonstrate that), not driving without reasonable consideration, not careless / dangerous driving.
• In the performance of the duties of that member.
• Where such use does not endanger the safety of road users.

http://www.irishstatutebook.ie/eli/2014/act/3/section/23/enacted/en/html

Amendment of section 87 of Act of 2010 — exemptions for emergency vehicles

23. Section 87 of the Act of 2010 is amended by substituting for subsection (1) the following:

“(1) Requirements under the Road Traffic Acts 1961 to 2010 relating to vehicles and requirements, restrictions and prohibitions relating to the driving and use of vehicles, other than those provided under sections 49, 50, 51A, 52 and 53 of the Principal Act, sections 12, 13 and 15 of the Act of 1994 and sections 4, 5, 11, 12 and 14 of this Act, do not apply to—

(a) the driving or use by a member of the Garda Síochána, an ambulance service (provided by a pre-hospital emergency care service provider recognised by the Pre-Hospital Emergency Care Council established by the Pre-Hospital Emergency Care Council (Establishment) Order 2000 ( S.I. No. 109 of 2000 )) or a fire brigade of a fire authority (within the meaning of the Fire Services Act 1981 ) of a vehicle in the performance of the duties of that member, or

(b) a person driving or using a vehicle under the direction of a member of the Garda Síochána,

where such use does not endanger the safety of road users.”.

The OP seems like he has an agenda.

I’d take his story with a pinch of salt. He was far too quick to in getting his bias out there.

What percentage of Garda drivers have passed the official advanced driving course? How are the ones who haven't passed it any better than a regular licensed driver?

Chief's authorisation has been done away with, however the actual exemption in the law is not qualified by holding the relevant qualifications (known as CBD2), that is a Garda Policy requirement and lack of such qualification does not invalidate the exemption, nor does it hold any detention/arrest for example of a suspect following a chase as unlawful.