Is it normal to get really hot wearing your wetsuit?

It might be that you haven't really properly put it on, being your first. You have to spend a lot of time getting as much material as you can up the legs and into your crotch, and then from the waist up as well.

For temps, everyone is different. 70 to me is very warm for a long swim and although I'd probably use it it's getting into non wetsuit territory

I'm comfortable (temperaturly speaking) with a water at 60ºF with my wetsuit at race pace. I can feel I'm sweating, not much, but I can feel the difference of temperature between my face and the water so I guess that I'm starting to sweat.

So I guess with 70ºF I will be more uncomfortable if I swim 'hard' with my wetsuit.

They actually predict between 62-66 degrees. Hopefully the cooler temperature will make the wetsuit situation more bearable!

You shouldn't be too hot at that temp in a wetsuit! As others have mentioned, everyone is different. In general, I would think that if you're getting uncomfortably hot in a wetsuit, you probably don't need it, unless you want it for flotation purposes or because everyone else is wearing one. If it's a matter of constriction, you might want to check that the size is correct and you're wearing it right; beyond that, swimming more in a suit tends to loosen up the arms a bit.

I have both a full wetsuit and a sleeveless shorty (covers only thighs). The latter is nice for "borderline" temps. I'm really cold-blooded so that's pretty much anything in the 70-76 degree range. 60's for me would be full wetsuit, and anything below that I probably wouldn't get in! A sleeveless shorty gives a lot more freedom of motion and on occasion I have even worn it in a pool if the water's really cold, and can do workouts with all four strokes. It also comes off a lot faster in transition than a full wetsuit, but still gives some buoyancy boost so you're not at too much of a disadvantage if others are in full suits. I think it's ideal for shorter swims (such as sprint distance) in water that's "just" cold enough for a wetsuit, or for OWS training in those conditions. My suit is made by an Oregon company called ProMotion but I think other companies might also make them.