Hello Pieanne!
"Have a go at" = "verbally attack". Quite informal:
1. He had a go at me for not having his dinner ready when he got home.
Or "attempt":
2. "Okay. So do you think you can manage to cook the dinner this time?" "Well, I'll have a go (at it)."
"Have a go on" = "have one's turn on", "use for one time", also quite informal, with implications o