Rabbits do make great pets and can easily be litter box trained, but that goes much more smoothly if they are neutered/spayed.
What are you keeping the rabbit in? The reason I'm asking is that you said you couldn't afford to buy a proper cage for the rabbit, and apparently you're having some kind of "hormonal issues" with the rabbit? You need to explain what you mean by that because the only way I know of to control rabbit hormones is to get it neutered or spayed. That being said, my point is that if you can't buy it a proper cage that is large enough for it, and you are just planning on letting it run around your house, if it's a male adult rabbit and is not neutered, it will spray all over the place. Even if you give it a litter box it will spray.
My dad has a "house rabbit". It's a male and is now about 6 years old. My young stepbrother wanted a dog, my dad didn't, and the "house rabbit" was my father's bright idea. They got BunBun when he was a tiny bunny and my dad thought he would just use the litter box automatically...Nope! Even after they trained him, which went pretty well actually, he still sprayed all over everything. As soon as they got him neutered he used only the litter box, just like a cat, and he's actually a great little pet.
What are you feeding it? It needs rabbit food/pellets, alfalfa or Timothy hay, and lots of fresh veggies and fruits, all daily. Plus a water bottle constantly full of fresh, clean water at all times. If you need any help or have questions just ask, I've babysat BunBun for weeks at a time, so I've got rabbit experience.
Also, make sure to take photos and take them to all your local shelters, rescues, and veterinarians. If the rabbit is that tame then it likely is a lost pet and someone, probably a child, is missing it badly.
FYI, rabbits that are outside are very prone to getting fleas, ticks, and warbles, which are disgusting and can eventually kill the rabbit, so please comb him to check for fleas/flea dirt, and then feel all over him for ticks and warble holes, especially under it's chin, in the skin wrinkles all around it's neck, and in it's armpits and groin areas. Warbles holes look like a perfectly circular hole right through the skin, and the warble that's inside must be pulled out. Hopefully you won't have the problem but it is really very common in outside rabbits.
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