I remembered my diablo achievements (hardcore runs), so i made a hardcore character. Yet, while descending on the lower levels, i fell into a trap with two crashing walls, which kills instantly if you do not pass between them very quickly. How is this trap bypassed? Are there any other ways to kill you instantly?? How to predict and avoid them???

Those traps aren't actually instant-kills, they just do a ridiculous amount of damage. If you go through at a high enough level you can survive them. It's still a good idea to avoid them, though.

Really that's about it, except for Dark Zealots at high levels. The Zealot lightning skill bypasses your armor and most of your resistances, and its base damage value is quite high. While not too much of a problem at first, its damage scales much faster than your health does, so at higher levels they will eventually be able to kill you in a single hit from offscreen. I'd highly recommend downloading the Dark Zealot Rebalance mod, which makes them much less frustrating at high levels.