For (1), I would just look at your picture and use the right-hand rule for cross products.
For (2), check this out.
I have 2 queries
1) Finding Lx, Ly and Lz in spherical co ordinates
Based on attached schematic its given that , , ,
How are these determined?
2) The unit vectors and are to be resolved into their cartesian components. I believe I can get (based on schematic and that )
but I dont know how to get the units vectors in terms of their cartesian components and
You're correct. However, that's not quite what they're doing. For one thing, they're dividing by the length. So, if you first compute
and then find its length, which is
on account of the range of (the polar angle on this website), then you'll find that
as they have. Does that make it clearer, perhaps?
or the SRSS's, as you abbreviated it. The subscript there on the norm symbol denotes the Euclidean norm.
In a more concrete fashion, think about the equation for a sphere of radius centered at the origin:
is also the magnitude of any vector going from the center of the sphere to a point on the sphere. The Euclidean length comes from that.