Crumbling bottom of a primavera

[Cfriedli]

We purchased house that has a built-in Primavera oven. The underside is crumbling and assume it needs to be repaired. the interior floor bricks are solid. It also seems to absorb moisture (i removed the front cover and chimney cap for picture) despite the front and chimney being covered when not in use . Any suggestions on how to repair? There is also a mildew smell inside when I uncover, can they be killed if I build a fire?