I believe the big nut has to come off. As far as length of the stud, you should get stock or atleast close to it. At a minimum it would have to be long enough to go through everything and still let the nut go on 100% and have the end of the stud flush with the nut for it. Get some PB Blaster and soak the big nut in it as soon as you can. Keep doing this(Overnight if you can) every couple of hours. Try tapping it with a hammer(use a chunk of wood or hard plastic between the big nut and the hammer so you dont damage the nut to try and loosen up the rust. Once it is off, make sure to anti-seize all of your lugnut bolts and this large one too. If I remember correctly there should be a cotter pin that you had to remove to get this out. Please make sure that there is nothing physically obstructing it to not come off. If you know how long your stock studs are, go to a tire that is on, measure how much the stud sticks out past the nut. Subtract that amount and that should give you the bare minimum length that you could use. I would recommend sticking with stock sizes here though. Good luck. If you have to take it to a shop, make them take all of your lugnuts off on the car if you have not had them off and also with the large hub nut on the other side of the car. Put anti seize on them all and put back together. This will help you in the future. So why did all of these snap on you? Is their any signs of wear or cracking on the rest? Usually, even if one is snapped, the other four are enough to hold it through normal driving. Were these torqued on too tight at one point?