Youll want to line the linoleum with fleece blankets so the rabbit doesnt slide around. Rabbits often wont run, some wont even walk, if they are on flooring that is even a little bit slippery. Sliding too much can also force cause splay leg, which hinders the rabbits movement all together
For neutering, most vets do it as soon as the rabbits testicles are descended. The surgery is fairly easy, but they will need to be on pain meds for about a week to help with healing. Spays are a little harder and generally cost a little more. Most vets wont do it until the rabbit is at least six months old, but ive heard a few do it at about four months old. Its harder on the females because the surgery is a bit more intense. She likely will be left sore for several days, and may need to be force fed if shes in too much pain/has too much stress to eat
For toys, anything wood or corn shavings my rabbits really like. I dont think corn shavings is too good for them, so they only get a toy like that on special occasions. Wood they can have whenever. My trio liked wooden/stick balls that they can toss around and nibble on. Weve tried thicker wood for them to chew, but its too big to throw, and they ignore those toys