How can magnetic flux be a scalar but magnetic flux density is a vector? I know flux is a scalar (slightly confused how this can be negative, as scalars don't take direction into account) but if flux density is flux*Area, how can multiplying be another scaler yield a vector?
 A: The area of a plane surface $A$ can by convention be considered to be a vector whose magnitude is $A$ and whose direction $\hat n$ is the direction of the perpendicular to the area.  $\vec A= A\,\hat n$.
If the area is a curved surface then one must consider small elements $dA$ which can be considered planar so $d\vec A =dA\,\hat n$.

The magnetic flux $\Phi$ is then defined as the product of the component of the magnetic flux density $\vec B$ which is perpendicular to surface $B_\perp$ and the area.
$\Phi = B_\perp \,dA = B \cos \phi\, dA=\vec B\cdot d\vec A$.  
The direction of the magnetic flux is defined by the choice of the direction of the normals to the surface.
In the diagram the magnetic flux is positive.
You can think of this as the magnetic field flowing through the surface in the arbitrarily chosen direction of the normals.
If the magnetic field was reversed in direction or the normals to the surface were in the opposite direction then the magnetic flux would be negative.
A: Flux is a concept borrowed from fluid mechanics.Supposecwe have a flow vector V1 entering into a volume through an area A1 and the flow vector is the velocity of water.The volume of water entering through that area in unit time is V1xA1.Now suppose there is another flow vectorV2 leaving that same volume through area A2 then the outflow is volume per unit time is V2xA2.Taking the difference tells us wuether the water is building up,is stagnant,or is depleting from the volume.If there are a number of inflows and outflows and we take all such products of inflows and there respective associated areas to be positive and all the products of outflows and therir respected areas to be negative then a summation of all of these tells us whether water is building up or depleting from the volume by observing it's sign.
The sign does not mean it is a vector but signifies whether  it is an inflow or outflow.
The product is called flux and is maximum in case the area and flow are perpendicular.When they are not perpendicular then the volume entering(or exiting)the are is from that portion of the area which is perpendicular to it ie found by the dot product considering the Area as a vector always pointed out of the volume.
