You should use "refractory mortar" to patch your firebox.
Refractory cements and raw materials are hard, heat resistant materials that are suitable for applications which require high temperature strength, wear resistance, electrical or thermal insulation, or other specialized characteristics. Refractory cements are used to patch or line furnaces and bond bricks or joints in high temperature applications. Most refractory cements consist of a mixture of a binder or clinker and a coarser aggregate.

Muratic acid should clean the brickwork up. Or, time...

I wouldn't wire brush it too much.