Can’t help you on that one, as I have kept away from all that stuff, although my British passport runs out soon and from a purely travel abroad viewpoint l can’t really see a reason to renew atm. I have 6 years left on my Irish passport
Depends if you want to stay longer than 90 days out of 180 days in the UK.
The same rules that apply to UK citizens in the EU will apply to EU citizens in the UK
(Unless some other special agreement is made, which in the case of Ireland is very likely)
I'd suggest you ensure that you keep both passports up to date