What goes up but never comes down?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

Can you find the mistake in the below statement?

How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it.

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

You can hear me, but you can't touch or see me.

What am I?

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

I have Rs.50 and I spend it in the way as below.

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

Can you decipher the two rows to find the hidden word?