2, 3, 5, 9, 17, _ What is the next number in the sequence?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Find the hidden panda in the image below.

John was piloting a plane behind a car but was never able to overtake it. Why?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

Which tank will fill first?

On a special event at the prison, 5 prisoners John, Jacob, Krist, Tang, and Dang given a chance to go to a sauna and can bring one thing with them.

Following are the things that the prisoners bring with them.
John: A soda
Jacob: Thermos
Krist: Book named "How to kill"
Tang: A Walkman
Dang: Harmonica

Since it is a Sauna, no one can see each other. After a while When the steam is switched, Tang was found dead and there was blood all around.
J Bond was called and he instantly come to know who can be the murderer. How?

What goes through cities and fields, but never moves?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?