Hi
"θα μπω" is the correct version and not "θά μπω". The word "θα" does not take an accent mark in modern Greek. It means "I will go in".
"Φέρε μού το" and "Φέρ' το μου" are both correct and they mean exactly the same: "Bring it to me".
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.