Question

For Faraday and Lenz's Law:

Did an increasing magnetic flux generate any current in the coil? decreasing flux?

Did the induced magnetic field always oppose the change in flux?

Answer 1

Faraday's law

the induced emf along any moving or fixes pathe in a constant or changing magentic field is equal to the rater at which the magnetic flux sweeps out across the path that is  

e = - d(phi)/dt

and from magnetic flux  

Phi = B*A cos theta

if the area is constnat then Faraday's law is  

e = - A dB/dt

if the coil has N turns then

e = -N*A dB/dt

and the coil having the resistance R then the changing magnetic field produces current in the coil

Lentz's Law

The induced current always opposes the change in magnetic flux , but not the flux

Did the induced magnetic field always oppose the change in flux? No the induced current opposes the change in magnetic flux

in Faraday's law e = -dphi/dt

the -ve sign indicates the polarity of the induced current