Hello!
I can not answer all your questions, but will answer the ones I can.
1. I'm planning to use 10 euros a day (5 for lodging, and 5 for food-can you really buy simple baguettes etc. for less than one euro?) on average. If I bivouac as much as possible (if possible, every other day) this is possible in the summer right?
In my opinion, this is cutting it too close. But as Falcon says, it is possible. You would definitely be more comfortable and safe if you doubled your budget.
2. Do Albergues really allow pilgrims (who are not lodging) to use the shower facilities and restrooms for 1~2 euros? There's a guy in Korea who says he traveled that way.
I saw this done a couple of times on the Camino Frances. I'm not so sure about the Northern Route, but I think you might be able to do it in MANY of the places I stayed (not all)
3. are the tap water safe to drink? I'm taking a LOT of green tea bags...
The water in Spain is perfectly safe to drink and probably much cleaner than the water we have in the USA! Avoid fountains that are labeled "NON-potable" but otherwise, feel safe.
4. I heard that the pilgrim passports you can get at key villages cost 1 euro. I don't really care about being certified. Would I still need the passport?
I would buy one. You will need a passport in order to stay in the alburgues AND to shower you will need to prove you are a pilgrim, not just a homeless person. Even if you do not sleep in them, you should stop and get your passport stamped to prove you've been there in case you need to spend a night in the next town. Plus, it is a wonderful momento!
5. I'm a 19-year-old, small Asian female (even for an Asian) I'm in pretty good shape though, and I'd trekked to Lhotse the year before. I'm planning to walk about 25 km~30km a day. Is this feasible? Especially if I want to avoid walking in the hottest parts of the day?
You should have no problems at all.
6. I promised to carry a cellphone so I can contact my parents in an emergency. Does anyone know an inexpensive way to get a phone that can dial internationally? (In my case, to Korea)
Somebody else will have to answer. I did not carry a phone.
Thanks! Hmm...I have way too many questions..