Learn French: C'est pareil pour moi. - It is the same for me.

Pareil means 'the same' or 'alike' when describing a general situation or when it stands alone. The phrase le même is usually attached to a noun (like 'the same car') or refers back to a specific object. Since 'It is the same' refers to a general feeling or situation here, pareil is the natural choice.

Could I say C'est le même pour moi instead?

You could, but it means something slightly different. C'est le même would mean 'It is the exact same one,' referring back to a specific masculine object you were just talking about (like a specific sandwich). C'est pareil simply means 'The situation is the same' or 'I feel the same way.'

Does pareil need to agree in gender or number here?

No. Because it is describing the neutral pronoun ce (the c' in c'est), it stays in its default masculine singular form. If you were describing a specific feminine noun, it would change to pareille (for example, une robe pareille for 'a similar dress').

Why do we use moi instead of me?