I am a full UK citizen and have been all of my life. I am

1.  There are no issues in having dual citizenship with an Irish passport as you need to be tax resident in Ireland if you are going to have to pay taxes there.  Essentially, this means that you must spend more than 183 days in Ireland in any one tax year or 280 days in any two years in Ireland.  So, there is no difficulty in having an \Irish passport and remaining living in England.  You will essentially retain your English domicile and tax status.  There is no obligation to file an anuual tax return just because you have an Irish passport.  So, there are no real issues which arise from having dual nationality, Irish and UK nationality.

2.  If you require clarification or if there is additional information you wish to share, I will be happy to assist further in the resolution of your Question.

3.  I cannot see that the UK Government will have any issues with you if you live on an Irish passport in somewhere like France for 4/5 months at a time.  The Irish passport allows you to stay as long as you want anywhere in the EU.  The British Government cannot prevent this.  So, you are just fortunate that you qualify for an Irish passport.