1. Once you're in Japan no one will be checking on where you're working or what you're doing. You should abide by the conditions of your visa if it says you shouldn't work longer than 3 months in any one job, however the reality is it wouldn't be enforced if you did.
2. So long as you've attended school in an English-speaking country for an extended period of time you'll be considered a native-English speaker. If you moved to Australia when you were 9, you'll be fine!
Having additional language skills helps for some jobs, although for English teaching it won't really matter. Being Asian in appearance won't matter. Most Japanese English teachers are too!
3. Usually they state you must be in Japan because they want you to have an appropriate visa already - meaning they don't need to sponsor you. On a Working Holiday Visa they won't have to sponsor you, so you can apply for jobs that require you to already have a visa. Some will want to interview you right away, for that being outside of Japan could be a problem. For others it won't be. That just depends on the position and the urgency with which they want to interview you in person for it.
4. If you are applying to a foreign-owned company, you should send a resume in the Western-style format. If you are applying for a position at a Japanese company, there's nothing wrong with sending a Japanese-style resume written in English and scanned.
A Working Holiday gives you the freedom to travel around Japan and try many types of jobs. Working at hotels, ski resorts, beach resorts, backpackers etc, are all possible on a Working Holiday, but aren't on regular Working Visas. I would recommend that rather than get straight into an English teaching job, you experience other types of jobs first, travel and have fun. You can always find a job willing to sponsor you a Working Visa and stay on in Japan long after your Working Holiday Visa ends if you wish. Search 'Resort Jobs in Japan' and you'll find heaps of fun opportunities.
Best of luck!