The nose one shouldn't make a difference at all (without mods) because there's no reentry heating in the game yet. Meaning stuff doens heat up when you go fast. So there's no reason it should have blown up att all, unless there was some kind of glitch.
Those "arrows" are the periapsis or inclination nodes. Move the mouse over it to see how low you're going to be, (periapsis) or the inclination (it'll say AN or DN) to see your relative inclination.
It is very much possible, albeit difficult and dangerous, because if the second stage is late in igniting, the rocket will start to tip over, and then start flying sideways.