What building has the most stories?

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

What is the word or phrase below?
R | E | A | D

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

Prove that the below maths equation is true.

8 + 8 = 91

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

John left on a horse on Thursday , was gone for two days, and came back on Thursday after completing his work. How did that happen?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?

I’m tall when I’m young, and I’m short when I’m old. What am I?