Well, in my area winters and summers aren't that extreme + the hutch is in shadowed area. The roof doesn't gets hot. She isn't a special pet rabbit (small one)- she's bigger (in Poland they'd call her medium rabbit or something like that). She's been keeped in a bit worse conditions i'd say (not hutch, but big cage with 5 other females only with hay and wheat.) Currently she eats fruits and veggies (beetroots leaves, grass, apples and corn. Tomorrow i'm getting hay and gonna try to get oat, as i have only wheat right now.). She doesn't trust me that much yet so i could pick her up. When she'll trust me more i'll let her out on the garden. For now (second day) she doesn't run away from me and lets me pet her a bit but still hides in the corner of cage when i'm trying (yesterday she didn't let me pet her). When she gets to trust me grandpa will ask one of his friends to let his male mate her). I hope for her to trust me in a few days

In very hot weather i may let her in some kind of improvised playpen in the basement, but it isn't much colder in my basement :/
I still don’t think it’s best for your rabbit to be outside unfortunately. When rabbits are outside, they end up not getting as much attention as they would if they are inside. But it sounds like you got the rabbit, so whenever I get an animal I am determined to keep it and care for it the best I can since it’s my responsibility. At least the weather isn’t as extreme where you live and the hutch is in shade. Over here, we usually have at least a 100 degree difference in summer to winter. Summers can get up to over 100 degrees and winters can get down to -25 degrees with wind chill. I’ll help you the best I can with my experience in having rabbits outside. The best hay you can provide for a rabbit is Timothy hay. I feed my rabbit grass hay mixed with alfalfa which is also good, but Timothy hay is a common choice as well. Hay should be fed freely. Never let her run out of it. Don’t let her eat too many fruits, it can be bad on her GI tract and possibly give her GI stasis (I’ve dealt with this probably 4 times now and sadly lost my rabbit to it). Veggies are a more nutritious and safer option. Of course, you can feed fruits but not too many. Good veggie and fruit choices include Romaine lettuce, red leaf lettuce, green leaf lettuce, spinach (not too much though), cabbage, bell pepper, cilantro (not too much), parsley (not too much), banana, strawberries, raspberries, etc. The one lettuce I advise you don’t feed is iceberg lettuce.
In the summer time, I would check on my rabbits about every hour to splash some nice cool water on them when it got hot. You can also provide them with a misting device that you can probably get at your local garden store if you’d rather. Make sure she has plenty of water and that she has a hideaway hut to go into (a cut out cardboard box will suffice). If she is on mesh, I recommend putting some tile slabs down, this will also cool her down and is much better for her feet.
In the winter time, water might get frozen so I refilled their water at least twice a day so they could have access to enough water without it getting frozen. You can also find insulators to keep the water from freezing. I would go to my local thrift store and get cheap fleece blankets to keep my rabbits warm enough and it’s easier on their feet as well. Provide her with a hidey hut as well so she can have an area to warm up.
For bonding with a rabbit, this takes time. You just got her, so I usually let my rabbit settle in for the first few days without too much stimulation going on. But once she’s settled in, try starting out with just sitting by her and letting her investigate you. Once she seems interested, start petting her and eventually you’ll be able to hold her. This would probably be over the course of several days or even weeks. It takes time! So don’t stress about it.
For breeding rabbits, I personally don’t see anything wrong with it. I know many people out there who are strongly against it but I have had two litters of baby bunnies and one of the two mothers lived for 7 years and had a good life. But, I don’t recommend overbreeding her. This stresses a rabbit out and can even shorten their lifespan. They can also get poor health. So if I were you, I would probably only let her have a litter once every 6 months AT MOST. That’s my opinion and I know others think differently. Rabbits are in heat all the time, never ending heat cycle. But I do have to warn you, if rabbits go unspayed by the age of 5, they have an 80% chance of getting uterus cancer. So I spayed the female that had a litter along with her baby, and the males. So all my rabbits ended up getting fixed and I truly believe it lengthened their lifespan. So just take that into account as well. On a more positive note though, having baby bunnies was pure joy and so much fun! If you do end up breeding her, it’s an amazing experience with little kits (baby bunnies).
On a side note, about the feeding, just make sure not to feed too many pellets. Don’t free feed them if you do feed her pellets. We feed our mini lop about two handfuls of pellets once a day. The rest of his diet is hay and veggies plus some little treats.
I hope she warms up to you soon! Please keep us updated.