"What is the difference between hydration & hydrolysis?
I know that hydration involves the [addition] of water ..."
That is the definition fo hydration, water adds to a molecule, either as H2O molecules (e.g., formation of a hydrate from an anhydrous compound), or as the components of water (H and OH) (e.g, the hydration of an alkene to form a saturated alcohol).
Hydrolysis involves the breaking of bonds in both water and the molecule, e.g., the hydrolysis of an ester to form the carboxylic acid and alcohol.
"... What is the name of the ester with only two carbon atoms? ..."
That's a little ambiguous. The ester with a total of two carbons is methyl formate, HCOOCH3.
The ester with two carbons in the acid and two carbons in the alcohol (four carbons total) would be ethyl acetate, CH3COOCH2CH3