Source Transformations
1) It isn't a 'Law' as much as it is a theorem, specifically Thevenin's theorem, stating that any network of resistors, voltage sources and/or current sources can be represented by a single ideal voltage source with a series resistance. There is also then the Norton equivalent circuit which represents any similar network as a current source and parallel resistance instead.

2) You can use it at any time in the types of network described earlier. The reason you get different answers in #6 and #7 is that you are looking at different things. There are a whole lot of different elements in the circuit which have been lumped together in different ways which are not necessarily related to any particular element in the original circuit. Essentially the idea of the transformation is that you don't care what is going on inside the 'black box', only what effect it has on your load.

To that end, you need to keep your load outside any transformations you do, make all transformations as if the load was just two unconnected terminals - but don't lose track of where those terminals are as at the end you will need to connect them back to your load for analysis.
For analysing the 8ohm resistance, you are aiming to get circuit #5 as it essentially boils the circuit down into a potential divider.