No, Magic Cylinder is not currently banned in the official TCG banlist. It is a legal card to use in most tournaments and games.
Complete banned lists are available here: http://www.wizards.com/Magic/Magazine/Article.aspx?x=judge/resources/banned
No it its going to be playing
The Magic Sword - 1962 is rated/received certificates of: Australia:G Finland:(Banned) France:U USA:Approved (PCA #19908)
No, note the difference between 'negate' and 'destroy'. When 'Magic Cylinder' activates, it doesn't matter what happens to the 'Magic Cylinder' card, it will not stop the activated effect from resolving. Chaining 'Dust Tornado' to it will do nothing. What you need is a card that will negate the effect too, such as 'Trap Jammer' or 'Solemn Judgment'.
They aren't banned in very many schools but if they are it is because American Christians have complained for years that the magic is evil and promotes witchcraft among children.
Yes. If Magic Cylinder or Dimension Wall's targets leave the field before they can resolve, they will not deal any damage.
Some people believe that the Harry Potter books should be banned because it involves magic and some Christians believe that magic is evil. Therefore all the characters in Harry Potter are evil because they can cast magic and they believe that God had told them to hate evil people and evil things.Not all Christians believe this.
Magic the Gathering has many formats, each with it's own list of legal cards. To see a complete list see here: http://www.wizards.com/Magic/Magazine/Article.aspx?x=judge/resources/banned
'Blistering Firecat' has long since rotated out of Standard format, but it has in no way ever been 'banned', and it can freely be used in any format that allows Onslaught-block cards.
Blue-Eyes Shining Dragon can negate effects that target it. Magic Cylinder is a targeting card, so yes, Blue-Eyes Shining Dragon can negate it.
No, magic eight balls are just black balls with a little cylinder like hole in the back with a small pyramid with words and blue dye in it. It's just luck that your question to the eight ball turns out right...not magic. You can buy Magic eight balls in many toy shops.
Magic Cylinder negates the attack. Since that attack never reaches the Damage Step (and thus there is not an 'end of the damage step') Axe Dragonute will not trigger and will not put itself into defence position.