Gortex speedo always works for me :-)
Always wear hiking boots with cushioned socks. They will keep your feet well cushioned and protected from the elements. I usually wear light weight shorts because we hike in the summertime, but if you are hiking during winter or on a route that has not been cleared you should think about wearing long pants (sweats or jeans). You can always wear long johns or leggings underneath if it is cold. You also should remember to layer your clothes when hiking. Start with a short sleeve shirt or cotton tank top and then add a second thicker layer (long or short sleeve) and always keep a jacket with you. Light weight is of course ideal but remember to pack appropriately for the season. Lastly, it is wise to bring a hat (preferably with a wide brim) along the trail. This can serve as a protection from sun and rain.
It depends on the time of year as was already said, but then it also depends on what mountains. Layers are always good, a hat is good, sunscreen is good, a day pack and lots of water are good.
It depends on the time of year.
A jet pack.