If your using a shed make sure it’s made using rabbit approved woods as bunnies will chew it. Also know that with sheds other creatures like spiders might try to occupy the same space as your bunny you you have to be extra vigilant.
I would look into garden sheds made of UNTREATED pine or Fur which will be really hard to find unless you find a nice local builder. Since its a large immovable place I would suggest grounded and not raised because something might want to meet underneath like a bunny or a predator so a concrete base would be good. As for construction you want it at least with barn doors so you can open the top and look inside to see your bunny. Without letting him out.
Since your shed is for an animal consider getting it double insulated meaning walls on the inside and outside with a space in this middle this will buffer extreme temperatures and ensure that the space isn’t filled with fiberglass or other insulation. For roof can be treated and built however you want but ensure water cannot pool on the top. For Windows full ones are not neccesary but some half Windows with some tint would be nice to keep the if out and the inside cool. You can even get slotted vents on the top to open and allow wind on a nice day and close for rain.
If it was me I would look into a small solar system that I could build that would power a small a.c. unit that I could set to emergency temperatures so it won t get too hot.
For cutting a hole in the side you can make a chicken coop size cut 18 inches high by 14 inches wide and make a small rivited plank for him to get outside. Possibly if you can save the spares to make a door to keep it shut when not in use so predators can’t get inside.
As for a fence outside I recently discovered rabbit runs by omlet and you can get a large area short top run with a heavy duty cover with a door to get access from the shed to the run. And can be secured to the ground with pegs to prevent foxes or rabbits escaping if you want some ideas I have some feel free to ask as I’m going to make a very nice outdoor space for my bun when I get a house
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