I found one small error so far...
You say:
It is useful to note that in order for this transaction to be valid the sum of the inputs need to be greater that the sum of the outputs.
This is not exactly true.
To be accurate you should either say:
It is useful to note that in order for this transaction to be valid the sum of the inputs need to be greater than or equal to the sum of the outputs.
or
It is useful to note that in order for this transaction to be valid the sum of the inputs must not be less than the sum of the outputs.
Additionally, there is a possibility of some confusion in your phrasing.
While unlikley, it is possible that a beginner might mistakenly believe that the phrases "sum of the inputs" and "sum of the outputs" mean "sum of the quantity" instead of "sum of the value". In otherwords, they might think that you have to have 2 or more inputs if you have 2 or more outputs.
As such, it might be better to use the phrases "sum of the values of the inputs" and "sum of the values of the outputs"