"Deutsch" (capitalised) is the name of the language - a noun.
And "deutsch" (lowercased) is an adverb, meaning "in a German way". It is also the basic form of the adjective, which you would use after the verb "to be", for example: "Dieses Buch ist deutsch", this book is German.
If you use the adjective before a noun, then it needs to take on the appropriate adjective endings, e.g. "ein deutscher Mann, eine deutsche Frau, ein deutsches Kind; deutsche Menschen".
You can also use the adjective as a noun, in which case it gets capitalised. It means "a German".
So, for example "ein Deutscher" (a German / a German man), "eine Deutsche" (a German woman); "der Deutsche" (the German / the German man), "die Deutsche" (the German woman); "Deutsche" (Germans / German people); "die Deutschen" (the Germans / the German people).
That's for the nominative case. In other cases, the endings will generally change.
No, not quite.
sprechen is the form used for wir (we, i.e. when speaking about ourselves = the speaker and others) as well as for sie (they, i.e. a group of people who are neither speaker nor listener) and also Sie (the polite way of addressing one or more listeners).
sprecht is the form used for ihr (the informal way to speak to more than one listener).
The form used when speaking informally to just one individual is (du) sprichst.
And spreche is only used when the subject is ich (I), i.e. when one person is speaking about themself.
Finally, there is also spricht which is for speaking about one other person who is neither speaker nor listener.
So in all, we have:
- ich spreche
- du sprichst
- er spricht / sie spricht / es spricht
- wir sprechen
- ihr sprecht
- sie sprechen / Sie sprechen
About the same as with "speak" and "talk" in English, I'd say.
I would only say "speak English / Englisch sprechen" (not usually "talk English / Englisch reden"), but in a context such as "speak about music / talk about music / über Musik sprechen / über Musik reden" I think they're fairly interchangeable.