Your hamster is probably just making the tubes more comfortable, and giving herself better traction to climb through them. If she comes back out of the tubes to eat and such, then she isn't stuck.
I think, if your hamster eats the food you give her, it must be fine because if she really didn't like it, she wouldn't eat it.
No.. She's just doing what her instincts are telling her to do. She's either doing it to help hide her food or to make a safe secure place for her to sleep... probably both.
In the wild, her ancestors would have back filled many of their tunnels to keep snakes and other predators from coming in and snooping around. She's just keeping herself busy doing what hamsters do. And as long as she's hording or eating the new food, than you can assume she likes it. Although they do have preferred foods, rodents aren't typically overly picky about the food they eat, so I wouldn't worry about it.