I went on this tour in July of 2022. I used a 38 liter, 2-wheeled, 4.5 lb empty bag. It weighed 20 lbs fully packed. It was often cold, wet, windy and rainy. I'd expect worse weather in April. Taking a long rain coat like this was probably the smartest thing I did. Sometimes hoods don't stay on in windy weather, but wearing a ball cap or a watch cap (beanie) under the hood will usually keep it in place. My major warm layer was a zip-up fleece jacket. You might need something a bit warmer than that.
1) Yes to both questions. Our hotel in Dingle did take a bag of laundry and have it done for us. So did the one in Belfast at the end of the trip. The cost was 20€ or 20£ and well worth the price. I'd spent a few days in Dublin before the tour started, so I did a little sink washing the first night in my tour hotel room. There was a laundromat nearby, but I really didn't need to use it. Based on my experience in Wales after the tour, whether I did laundry myself in a laundromat or had it picked up from my hotel, the cost was 20£.
2) Just say "no" to fancy clothes. I had my normal travel clothes and shoes on the whole time and never felt under-dressed. I actually plan my travel wardrobe around a colorful, not expensive, not silk scarf. On this tour, my basic colors were yellow, blue and orange. A good thing about a scarf is that it can protect a top from food spills and is easily washed and dried overnight. Including what I wear on the plane, basic garments for my trips include 3 pairs of long pants and 6-8 tops, period.
3) If your hiking shoes prevent slipping and support your ankles, if your pants cover the tops of them and if you wear socks that will keep your feet warm and dry, I'd say you're well-prepared for footwear. Be aware that the tour may spend more time on slightly hilly, rough or wet terrain, even in towns, than you expect. I've been wearing a pair of KEEN Women's Terradora 2 Mid Waterproof Hiking Boots on my trips for years. I like them because they're lightweight and support my ankles. I have them in 2 colors including my favorite blue ones called Majolica/ Tapestry. I always take 3 pairs of fun moderate compression Sockwell socks to wear with them. They support my legs, help to prevent fatigue and keep my feet warm and dry. I do pack a pair of comfy Abeo flats, but I rarely wear them outside the hotel. After staying in a B&B with a very slippery shower floor, I always take a pair of nonslip fast drying shower shoes similar to these. I wear size 10 and they easily fold small enough to fit in a quart size Ziploc freezer bag.
One final note. The one time I wore neutrals on a trip, I found it boring and depressing. One woman on this tour with me did that because she thought it was expected and regretted it. If neutrals work for you, that's great. If not, don't be afraid of showing your personality in what you wear.