The $E$ inside a filled conductor is said to be zero only when at any point inside the closed surface the resultant of $E$ is $0$.
inside the inner conductor net electric field will always be zero because whole of the charge will reside only on its surface .(why)?
the reason is if there is any net $E$ at any point inside the inner conductor it will immediately pull the electrons in the opposite direction of $E$ due to charge on surface will increase which will decrease the $E$ which was present. the surface of conductor will absorb all the charge in such a way that net $E$ at any point inside inner conductor becomes zero.
1.Inside it is zero, but outside it is present and that too only tangential(i suspect it is tangential)?
remember the outer conductor has a hollow region and an another conductor inside it.if you consider a hypothetical gaussian surface enclosing the inner conductor only then there will be a net $E$ flux through that gaussian surface.this implies that resultant $E$ at points which lies on hollow region is not $0$.
Due to -ve charged inner conductor the +ve charge existing upon outer conductor will be attracted towards inner conductor .if -ve charge is more than +ve then the +ve charge on outer conductor will reside upon its inner surface and vice-verca.
2.Due to -ve charge on inner conductor there will be a net $E$ inside the outer conductor because of net charge inside outer conductor i.e $E$ inside the outer conductor is not $0$ in such case.