when an event is drawn that affects the whole land for two turns where do you place the card, does it stay on the board in the space drawn or does it go off the board?

I say it stays at the space where it was drawn

Anywhere you want. Technically, it should go to the discard pile after being drawn, but events like that (Blizzard, Prophecy) I place on the CoC as a reminder that they are happening, until the duration has expired.

The space. This is the correct procedure!

Ell.

Canadianized said:

Cards are discarded only when their effect has expired, as clearly written on them (have a closer look at Blizzard and Prophecy). For all Turns an Event does affect the game, it stays on the space where it has been drawn and counts as a face-up card for that space.

You're just following the rule as written (page 7):

When drawn, Adventure Cards are taken from the top of the Adventure deck and placed, faceup, in the space where they are encountered.

If event cards stay on space what if another character encounter it second time. Does the effect continues longer? In such case Blizzard or Dark Denizens can occur again and again...

Croonos said:

No, it's there just as a reminder, but also to count against the number of cards you draw. Otherwise, the Blizzard would never end: Blizzard-> adjacent space -> back to Blizzard (if you wanted to).

Neverending Blizzard... sounds cool. Brings back memories of the movie Legend.