Can all the Native American people speak Quechua ?

Answer 1

No... Quechua is spoken in Peru. Native Americans in other countries will not know Quechua.
There are many native American languages, like Cherokee or Navajo, for example. Often, each tribe/community will have its own language.

Answer 2

Of course not!
That's like asking if all white people speak Polish!

Quechua is the language spoken by the people who were part of the Incan empire. Other languages still commonly spoken:
Nahuatl - Descended from the Aztecs (1.5 million speakers)
Cherokee - Retained largely for cultural reasons (~30,000)
Navajo - Highly unlike most other Indian languages, it is highly inflected and was used as a secret code during WW2 (200,000)
Guarani - Spoken around Paraguay. Even a large number of white people learned and speak this language (7 million)

Native American languages are highly different from each other - there are many language families. That means that most Indian languages less closely related to each other than English is to Hindi (both are Indo-European), though of course there are groups of similar tongues.

This gives a good overview of the languages:
http://www.indians.org/welker/americas.htm

Then, there's always wiki:
http://en.wikipedia.org/wiki/Native_American_Languages

Answer 3

Every Native Nation has it's own language....so no. That's like asking if all whites speak the same language...

Answer 4

no