Hi there and welcome. I'm not a flemmish owner but I'll answer some questions anyway
-You can feed her alfalfa hay until about 6 months old at which point you should change to Timothy. But you can just use timothy from the beginning too.
-I give Bandit two fresh servings of hay a day (large amounts almost as big as he is). He hasn't always finished the last amount but he seems to enjoy the "fresh" hay better. She will need hay available at all times, so give her plenty. If you wanted to clean out the old hay, once a week would probably do it.
-Bedding is not needed or often recommended for rabbits. Rabbits can be litter trained and if you want a litter box in the hutch, having bedding elsewhere will just serve to confuse her. However, if you do want to use bedding, you can use hay, or even fleece blankets (fleece is fine, towels are not because of the long fibres) or something like carefresh. Many people use wood stove pellets for litter.
-At this age, unlimited pellets are the way to go, as she hits about 6 months, perhaps a little older like 9 months (as flemmies take longer to reach full size) you will want to start limiting them. The recommended adult amount is usually about 1/4 -1/2 cup of pellets per 5 pounds of rabbit a day.
-There is much contradicting information on treats, but to avoid stomach upsets most people say not to introduce treats and greens until at least 3-6 months of age. Some rabbits tolerate it better than others so you could try introducing very, very slowly at 3 months and if her stomach gets upset wait a month before trying again.
-Rabbits handle the cold much better than they do heat. They have that lovely fur coat after all. Many people keep their rabbits outdoors during winter, even with snow, you just have to make sure they're protected from the wind and rain and snow obviously. It would be good to provide lots of bedding during winter if they will be outdoors at this time.
-I would not buy that playpen, it is going to get chewed on and dug through and your bunny will be out and about in no time
If you have a hallway or similar area that you're ok with your rabbit being out in you can use baby gates to fence her off. Otherwise, the metal playpens are the best options, you can always put a heavy duty tarpaulin or rubber or foam mats underneath to protect the flooring and you can adjust the space to fit your space however you like. As for the size of an indoor hutch, in any case with rabbits, as big as you can make it is best. I've heard of a "rule" that mentions having a cage/hutch that is at least three hops long and two hops wide (obviously as your rabbit grows this will change) but if you can fit/afford a bigger cage, then get as big as you can go, your rabbit will appreciate it
-She should get the same amount of exercise year round, bunnies love having time out to run and jump and play and I find the more you give them, the more rewarding it is.
-The only other thing I can think of, is that if you're having her outside in a hutch, it's a good idea to have the hutch or at least a second level of the hutch raised off of the ground so that the bunny is higher than any potential predators. Also, even if the hutch has a shaded/hidey hole part, it should be placed in the shade, otherwise they can get much too hot in the sun.
Hope that helps