Is Gajeel and rouge brothers?

no gajeel is only rogues idol

No.
Rogue really looked up to Gajeel when he was young, and thought of Gajeel as an older brother. They aren't actually related.

It's hard to say, because during the Grand Magic Games when Gajeel and Rogue were against each other, Gajeel said,
"First of all his name isn't Rogue it's Lios and he's my sworn brother!"
At first I didn't understand what Gajeel meant sa pamamagitan ng that, and still don't know what he meant sa pamamagitan ng that.