A PE is defined in The OCED model treaty Art 5. This will be replicated in the UK/Ire DTA. Based on the work you are doing, just ensure the place of management of your company (by holding no company meetings in Ireland, etc) remains in the UK and you should not be regarded as trading through a PE. PE specifically includes place of management, branches, offices, factories, workshops, etc - see Art 5 for full list. From what you have described, I don't think you will be operating from a PE.
Your company is resident in the UK, business profits from non PE operations in Ireland will be taxed only in the UK.
As regards personal, you are UK resident and will remain so, unless you exceed 183 days in the tax year. So as a non-resident, you are Liable to Irish tax on Irish source income only i.e. Irish deposit interest, Irish employment income (Ok with UK employment income), irish rental income, etc. And remember its presence at any time of the day counts as day.