Why does water rise in the tube?
Because part of the air has been consumed: Oxygen.
Rust is iron(III)oxide trihydrate. Formula?
Rust = Iron(III)oxide trihydrate = $Fe_2O_3\cdot3H_2O$.
Write down the equation of this reaction!
$4Fe$ $+$ $3O_2$ $+$ $6H_2O$ $\longrightarrow$ $2Fe_2O_3\cdot3H_2O $.
What is this type of reaction?
It's an oxidation.