Wow, what a lot of questions!
1. Yes, that's normal
2. It depends if it's a Syrian or dwarf hamster. As long as you provide things for you hamster to chew on (such as mineral blocks, soft untreated wood, toys etc.) they shouldn't get too long.
3. As long as you try to keep it clean it should be okay. If it doesn't heal or gets worse she should go to a vets.
4. You probably wouldn't be able to see the actual lice, but the hamster would be scratching a lot, have flaky skin, red patches on the skin and spots and small wounds.
5. That depends.....has it always been brown or has this just appeared recently?
6. It really, really depends on where you live and what vet you go to, it varies enormously. It wouldn't be expensive for a hamster though.
7. You can't really tell a hamster's age, it's extremely difficult to do as they only live about 3 years.
8. This could be due to lack of water or nutrients. Make sure he/she always has fresh, clean water available and is on a good, complete hamster food. It's also probably worth getting it checked out by a vet.
9. Yes, hamsters can eat pear
10. As hamsters are so small, it's very difficult and quite dangerous to bath them. The best thing to do is brush them with a clean, moistened toothbrush.