What does this mathematical rebus means ?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

You need to move three matchsticks to form three squares. Can you do it?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

Here is what you have to do. You have to throw a ball as hard as you can but it must return back to you even if it does not bounce at anything. Also, you have nothing attached to the ball. There is no one on the other end to catch that ball and throw it back at you.

How will you do it?

What English word has three consecutive double letters?

With the help clues provided in the image, can you find the 5 digit key?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?