Che / cosa / che cosa? When to use which
What I think is the following:
'Che' is for questions where you want to know something about a certain noun, like 'che ora', 'che colore', 'che giorno', etc.
'Cosa' is for when you don't really know anything yet, and the answer isn't restricted to a certain category. 'Cosa è questo?', 'Cosa ti piace?'
The only way I know how to use 'che cosa' is simply when saying 'Che cosa?' if you didn't hear someone properly, for example.
Is the above right? Did it make sense or am I just making stuff up?

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Andrew put two fingers on the heart of the matter.
I) If you have already a noun you use only "che" (a) (b), otherwise you use "che cosa" (c) (d) (e)
II) You had to use the preposition required by the verb in front of "che cosa" (e)
e) "di (che) cosa vuoi parlare?" [parlare] "di" sth.
f) "a (che) cosa stai pensando?" [pensare] "a" sth.
g) "da (che) cosa stai scappando?" [scappare] "da" sth.
...

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Your post is correct but not completely.
'Che' could be used with a double meaning: 1) "dichiarative": you use 'che' when you want to explain, declare something e.g: "Mi è stato detto che eri in casa" and it corrisponds to 'that' in English.
2) "Interrogative": as the word says, you use it in questions. E.g: "Che ore sono?"
Your post about 'Cosa' is quite correct but remember that 'Cosa' is also a noun! ( una cosa di questo genere)
Of course, you usally  use 'che cosa' in the questions, because you don't know anything and you want some explanations.

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Examples:
a) che film vuoi vedere ?
b) che libri hai comprato ?
c) che cosa vuoi mangiare ?
d) che cosa hai detto ?
e) di cosa vuoi parlare ?

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Che, cosa e che cosa, utilizzati come interrogativi, sono intercambiabili. 
Quale fra loro viene utilizzato dipende dalla regione in cui ti trovi, ma non ci sono differenze rilevanti.

Che, cosa and che cosa, used as question words, are interchangeable.
There aren't considerable differences, the use just depends on the Italian regions.