What has to be broken before you can use it?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

Can you count the number of triangles in the given picture?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

What happened when the wheel was invented?

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?