How we cite our quotes: All quotations are from The Two Towers.
Quote #4
GOLLUM: It tries to chokes us! We can't eats Hobbit food! We must starve!
SAM: Well starve then, and good riddance!
GOLLUM: Oh, cruel Hobbit. It does not care if we be hungry, does not care if we should die. Not like master; master cares; master knows. Yes, Precious. Once it takes hold of us it never lets go.
Frodo has earned Gollum's loyalty by caring about him. But why does Frodo care? Gollum seems to know the genesis of Frodo's empathy better than Frodo does. It's the Ring. Gollum and Frodo have both been taken hold of by "the Precious," although we'd hardly call their obsession with it loyalty.
Quote #5
GANDALF: Do not regret your decision to leave him. Frodo must finish this task alone.
ARAGORN: He's not alone. Sam went with him.
GANDALF: Did he? Did he, indeed? Good, yes, very good.
Gandalf is very pleased by the news that Frodo has a companion. Gandalf was the one who made Sam accompany Frodo in the first place and knows how loyal he is to Frodo. This close bond between the two hobbits is going to be more and more important as Frodo is pulled deeper into the lonely hold of the Ring.
Quote #6
GOLLUM: There's another way, more secret. A dark way.
SAM: Why haven't you spoken of this before?
GOLLUM: Because master did not ask.
SAM: He's up to something.
FRODO: Are you saying there's another way into Mordor?
GOLLUM: Yes. There's a path, and some stairs, and then… a tunnel. FRODO: He's led us this far, Sam.
SAM: Mr. Frodo, no.
FRODO: He's been true to his word.
SAM: No.
FRODO: Lead the way, Sméagol.
GOLLUM: Good Sméagol always helps.
There are so many things at play here. First, we have Sam questioning Sméagol's loyalty to Frodo in contention with his loyalty to the Ring (it is a bit suspicious that Sméagol hasn't mentioned this alternate route). Then we have Frodo deciding to trust Sméagol based on the fact that he's been loyal so far. In doing this, Frodo ignores Sam's counsel and seems to be himself more loyal to Sméagol than to Sam. But is Sméagol really trying to help, or has he already developed a plan to bring them to her? And what about Frodo? Is he delaying his venture into Mordor because he has grown fonder of the Ring? His loyalty is still to his mission and the fellowship and all of the free world, right?