You ask difficult questions. I've been visiting Dominica for about 14 years, and have done extensive research into its history and nature.
I've stayed all over the island, and do more rainforest and nature exploration than diving, though I at least snorkel every day. I'll be there for most of this coming April, renting a private house a few miles outside Roseau. I also rent a 4wd vehicle (a small Suzuki) for the entire time I'm there, picking it up at Melville Hall airport when I arrive and dropping it off there when I leave. I don't suggest driving there unless you are ready for some of the most daunting, steep corkscrew roads in the world, and driving on the left on very narrow roads often hacked out of a sheer mountainside. Having your own vehicle is the best way to really see the island, which is almost supernaturally beautiful in a sometimes dark brooding way.
The weather there is completely unpredictable. It can (and does) rain almost anytime, almost always briefly. you can feel and smell the ground and the lush vegetation inhaling it, and glistening in 100 shades of green afterward. Jan-March are the driest months, but I've experienced torrential downpours every month I've been there, including the dry months. I didn't mind at all. Very often the sun continues to shine while it's raining. Sometimes you get these strange misty rains, almost like God was misting his garden through multiple simultaneous rainbows.
It rains a lot in Dominica, more in the June to November period than other times, but there is not a huge difference, except for mid summer/early fall when it rains quite a bit. But that's when the mangos and other delights come into season, in places covering the ground. In places where they grow wild you can just pick them up and eat them.
For that and other reasons June is my favorite month on Dominica. The reefs are alive with baby fishes, the high forests echo to the cries of young fledgling parrots, and the island itself seems to be pulsating with life. June can be wet. So can July. So can April and May. It's different every year, even every week.
Dominica is a rainy island. The landscape is more vertical than horizontal, and the seemingly countless mountains draw in the rain clouds. In rains MUCH more in the interior than along the coast, literally 5 or 6 times as much. That's why they still have a rain forest big enough and dense enough to get lost and die in. From the air it looks like the island is one big forest, and that's not far from the truth.
Diving in the extreme south is better. The giant crater that constitutes the Caribbean side in the south is amazing. Mid island diving on the patch reefs is great fun, though not 'high voltage' like the south. The north is less exciting unless you go way offshore, which can be dangerous unless you are a highly experienced expert diver. Dominica is not a coral island. No long sandy beaches. The mountains plunge straight into the sea, resulting in depths of several hundred feet only a few hundred yards off the shore in some places. That's what brings the big whales in.
Stay on the Caribbean side. Less rain, calm seas. The Atlantic side currents can drown you in a trice. That's why the Caribs built their final refuges there. Boats can't land easily, if at all.
There are mosquitos in the summer, but they are not as bad as on most other islands. There are fewer than here in NJ in summer, so I can't say there is a serious bug problem. But there are also lightening bugs the size of small birds and big beautiful beetles to counterbalance the mosquitos, which are not that bad. Bring deet. I don't use the nets at all. they are there because few rooms have screens in the windows, to catch the tradewinds.
There is excellent hiking all over the island. Everywhere. There are only about 70,000 residents on the entire island. Just north and east of Portsmouth is some magnificent country.
Roseau has somewhat better weather than Portsmouth, which can get rather windy too.
Dominica requires that you have an intrepid spirit, especially if you go off on your own. I'm 71, and I do all my own driving, exploring, and hiking because I know the place like a second home. It's not a place for those who need to be taken care of, or looked after. Except for the horrible boatloads of cruise ship one-day visitors there are very few tourists there. Very few. The place is not really set up for tourists, except around the cruise ship dock in Roseau, which I'd stay away from. People are pleasant, but they are mostly independent of tourist concerns. You have to find your own way. Guides are available, though, and probably worthwhile, especially if you don't have your own transportation and a tough adventurous attitude.
I really love the place, but it is not for everyone. The island demands a lot from you. It gives a lot back, but never on a silver platter.