What is the biggest age gap permitted by halakha between a man and a girl/woman for them to get married?
There is no age gap explicitly mentioned in halacha. However, there is a general depreciation in The Talmud for marrying two people of significantly different ages.
"Who marries his daughter to an old man, or who takes an old woman as a wife for a young son, to him the verse refers, "To add drunkenness to thirst; the Lord will not pardon him" (Deuteronomy 29. 19f) (Sanhedrin 76b).
"If he was young and she old, or vice versa, they [the elders] would say to him "What sense is there in your marrying one much younger than yourself? or "What sense is there in your marrying one much older than yourself? Go, marry one who is about your own age and do not introduce strife into your house" (Jebamoth 101b).