A brief respite for the hobbits, traveling in lands less touched by Mordor. Sam is ever pragmatic starts thinking about food, and the necessity of more to even reach their destination, let alone maybe make it home. Maybe they have a chance? Sam more than anyone is incredibly pragmatic. After all, even if they are on an impossible quest, food is necessary until althe bitter end. Asking Gollum to hunt them a rabbit reflects on that pragmatism, his love for Frodo, and the direness of the situation.
"I does ask. And if that isn't nice enough, I begs."
The relationship between Sam and Frodo has always been an interesting one. Technically, Frodo is Sam's master, but there's always been more between them. There's more to Frodo than when they started with everything that has touched him, and the nature of their relationships shifts along with it all. A few quotes to think about things:
"He was reminded suddenly of Frodo as he had lain, asleep in the house of Elrond, after his deadly wound. Then as he had kept watch Sam had noticed that at times a light seemed to be shining faintly within; but now the light was even clearer and stronger."
"I love him. He's like that, and sometimes it shines through, somehow. But I love him, whether or no."
"Gollum returned quietly and peered over Sam's shoulder. Looking at Frodo, he shut his eyes and crawled away without a sound."
I'm not sure exactly what they're seeing. Perhaps it's akin to the glow the elves possess, or a blessing of some sort? We know Gollum finds things such as the elven rope painful to touch, so perhaps there's a similar agency touching Frodo.
Of course hobbits are generally skilled in the art of cooking, food is so important to their lives. A small detail that might not stand out to most readers is that Tolkien understands the importance of salt. "And hidden at the bottom of the pack in a flat wooden box a dwindling treasure, some salt." It's not just a seasoning, though needed less with meat than with other foods, salt is necessary for survival and in the pre-industrial fantasy world of Middle Earth, a very expensive and precious commodity. For context, the words "soldier" and "salary" originally derive from the same root from when the Romans paid their fighters in salt. Salt is serious business (I recommend reading Salt : a world history). Rabbit is actually probably the worst game meat they could be eating due to how lean it is, but Sam knows his craft and does what he can to make it a proper meal instead of just rabbit alone.
He is cruel to Gollum. I'm not sure if he is overly cruel or if due to their mutual antagonism that was the only way to get what was needed? I do think Sam's is wise to avoid leaving Frodo with Gollum alone.
In the end, Sam's fire leads Faramir and his men to them. Faramir knows of Boromir's dream, of the answers that he sought in Rivendell. Not only that, but these men are Dunedain, Rangers.
The focus here in the film remains on the antagonism and disgust between Sam and Gollum, rather than the more complex relationship in the book. A few of the key dialog interactions are kept, but instead we see Gollum courting Frodo's favor, the grounds for his more overt attempts to replace Sam. The Gollum of the films is perhaps a bit crazier, but also more cunning than the one in the books. Yes, he is a bit too fond of raw meat for hobbit tastes, but exerting an effort on his own volition to hunt down food specifically for Frodo stands out as a very significant action. And then Sam goes and 'ruins' the present.
Faramir and the Rangers pull off their ambush before the hobbits are discovered (and taken into custody). The decision to end the scene there and cut to Gimli chatting (and possibly flirting) with Eowyn makes for fantastic conflict of tensions, which is why I'm assuming they mixed up the order. But man, it's a long time before we come back to our hobbits. They're caught by (or run into) Rangers in Scene 23. Scene 32 we go back to Faramir over maps making battle plans, then eventually get to the hobbits who are accused of being orcish spies, and a general blending of the next two chapters into this one. I'm not sure why Frodo flat out lies about Gollum, his answer in the book was significantly stronger and was at least half true. Maybe the influence of the Ring?