Learn French: Nous mélangeons beaucoup de riz avec un peu de viande.

After expressions of quantity like beaucoup (a lot) and un peu (a little), French always uses a simple de (or d' before a vowel). You drop the usual words for "the" (le, la, les). So, instead of combining de and le to make du, you just use de.

Does the same quantity rule apply to un peu de viande?

Exactly! Even though meat is feminine in French (la viande), the quantity expression overrides the normal rules. You use a plain de after un peu, never de la.

Why is there an extra 'e' in mélangeons? Shouldn't the ending for nous just be "-ons"?

You are right about the standard ending! However, mélanger (to mix) ends in "-ger". If we just added "-ons" to make "mélangons", the letter 'g' would make a hard sound (like in the English word "go"). To keep the soft 'g' sound (like in "mirage"), we have to keep the 'e' before the 'o'.

Do I pronounce the 'z' at the end of riz?

No, the 'z' at the end of riz is completely silent. The word sounds just like the English word "ree".