For expanding the eco-earth, just get a tupperware container or a plastic bucket or something, put the brick in there, and use the treated water to expand it. You can break it up if you need to.
Frogs will blink, but they should not be sitting with their eyes closed or half-closed for long periods of time, even asleep. Can you post a picture of this?
Even though the person you got her from has been feeding frogs and fish, you really need to try and get her on a healthier diet. Feeder fish from pet stores are almost always diseased; if you ever want to give her fish, buy a pack of frozen silversides. As for the mice, it can be very dangerous to put a full grown mouse in with a frog. I really wouldn't recommend doing this again. Frogs' skin is very fragile so even a small bite or scratch from a mouse can damage it greatly.
Also, even large pacs shouldn't really be eating anything much larger than a fuzzy mouse. The hair and claws on mice don't digest well, and this is a big impaction risk. I never recommend feeding anything other than pinkies because of this (paranoid about impaction).
If the frog won't take nightcrawlers or other insects, you can try taking the insect in tongs and rubbing it on her lips. She will probably get annoyed after a few minutes and take it. Once they realize it is food, they will take it more easily.
Thanks for doing research on your pet! She's a very nice looking frog

Yes, these frogs can draw blood with their bite. You're doing right, not handling her. The less stress until she gets used to her new home, the better.