You will have to go through immigration, I believe, since you are arriving into the EU. Good advice about getting a seat near the front of the plane to minimize the number of people in front of you at passport control/immigration.
The terminals are connected and about a 15 min walk.
3 hrs is easily enough time especially if you don't have to check in a bag.
Ryanair is great if you know what you are getting into and you play by their rules. One of those is you MUST check in (online) at least 4 hours before the flight. You can do it quite far in advance if you pay to choose a seat, but you can do it about a week in advance without paying. Either print the boarding card or use the Ryanair App to store it on your phone. This works quite well and any scanners at the airport are set up to use it. They will charge you if you haven't checked in in advance. They will allocate you a seat unless you pay to choose one in advance.
The cost to check in a bag is different depending on whether you book it in advance, or you turn up and they force you to check it in because its too big/heavy. My experience is that they rarely weigh the bag, but if it looks quite fat and big they may ask you to check it at the wireframe size checker thing. Not sure about hiking pole philosophy. Usual airport things like liquids of 100mls or less are permitted in a clear plastic bag. We usually bring an empty water bottle, and then fill it up at a water fountain after security. Water in airports is usually outrageously priced, but you can get a 500mls bottle for 1€; there is even an honesty box for you to drop the euro into.
There used to be a queue that formed quite quickly to get on first on the plane and choose a seat. Now that they allocate seats, there is still a queue that forms at some point, because the overhead locker space is relatively limited, and you want to have your bag close to you. If the flight is full, they will go through the queue trying to put peoples bags in the hold (for free). I usually tell them I have a tight schedule at the other end and need to get off quickly. Most times that is true
I would reckon that the chances of the Dublin -Biarritz flight being seriously altered are slim, and the transatlantic ones less so, although it can still get delayed. If you do miss it, Ryanair will not have any sympathy and they don't do connecting flights, so if you miss the Ryanair flight you will have to book a seat on the next flight (if there is room). They only flt once a day and every Tuesday, Thursday and Saturday, so you would have a 2 day wait.
Bottom line:
If it was me, I would go for it, 3 hours is plenty
What dates are you thinking of?
If necessary and I am around, Plan B could involve bunking down in my place.