What is both possible and impossible at the same time?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G

What does a man do only once in his lifetime, but women do once a year after they are 29?

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M

Spot the cat in the picture below

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

How can you tell a raw egg from a hard-boiled egg?

What is the word or phrase?