Learn Romanian: Îmi dai o mână de ajutor?

Îmi is the indirect object pronoun meaning 'to me' (Dative case), because you are giving a hand to me. Mă is the direct object pronoun meaning 'me' (Accusative case), which would be used if I were the actual thing being given!

The translation says 'Can you give', but there is no word for 'can' (poți) in the Romanian sentence. Why?

In Romanian, it is very common to use the simple present tense to make polite requests or offers, without needing the verb a putea (to be able to / can). You are literally just asking 'Do you give me a hand?'.

Is o mână de ajutor a set phrase in Romanian?

Yes, it is the exact equivalent of the English idiom 'a helping hand'. Literally translated, it means 'a hand of help'.

Why do we need the preposition de before ajutor?

In Romanian, the preposition de is frequently used to connect two nouns when the second noun describes the first one. Here, de ajutor acts like an adjective describing what kind of hand it is (a hand of help).