Why does it say "va'Ynasu Kel"?
Radak (17): They should have realized that just like He was able to take water out of a dry rock and bring down manna from the air, so He can bring to them meat in the Midbar. They did not think so, and tested if He can do so, at Kivros ha'Ta'avah.
Why does it say "bi'Lvavam"?
Radak: It was in their thoughts. They asked for meat to test Him, for the manna was a good, pleasant food; they did not need meat. They thought to test him, but did not say so with their mouths; rather, they said that they need meat, and disgraced the manna - "Nafshenu Yeveshah Ein Kol Bilti El ha'Man Eineinu", "v'Nafshenu Katzah ba'Lechem ha'Kelokel" (Bamidbar 11:6, 21:5).
Malbim: Really, they did not crave meat; they wanted to test Hashem. They did not believe that His power is unlimited, and He can fulfill His promised to dispossess the Kena'anim. When he first gave manna, Slav descended with it - "Bein ha'Arbayim Tochlu Vasar uva'Boker Tisbe'u Lachem" (Shemos 16:12). However, the Slav ceased when they reached Refidim. There He brought to them water. Yisrael thought that His power is limited; He cannot supply three things (water, bread and meat) at once 1 .
Malbim: One whose power is limited and it is not from himself, there is a limit to how many things he can do at once. E.g. Eliyahu could not hold the key for rain and for Techiyas ha'Mesim at once (Sanhedrin 113a).
What is the meaning of "l'Nafsham"?
Radak: For their desire 1 , like it says "His'avu Ta'avah" (Bamidbar 11:4). The Nefesh has Ta'avah - "Ki Te'aveh Nafshecha Le'echol Basar" (Devarim 12:20).
