I wouldn't worry about the religious aspect of it too much. Most Japanese people are fairly non-denominational, many practicing both
Shinto and Buddhist traditions.
Also, there's a Christian high school near my house that my friend goes to. As far as I can tell, the only thing significantly Christian about it is they have mass in the morning for about 50 minues. Not preaching, but studying the bible, which is good for general knowledge in itself.
However, it being an International Christian school, and if that's one of its main selling points, then religion might be stressed a little more. Can you read Japanese? If you can't, you can post the webpage and some of the forum members might do a little snooping for you.
I don't know about scholarships, but a part-time job should be okay. providing you're a legal resident. As a high school exchange student, I can't, but I think college students might be able to.
w ww.police.pref.gunma .jp/keijibu/01keisou/kokusai/01-fuhousyurou.htm
w ww.landbrains.co.jp/t abunka/english/01.html
I suggest you look at these. One is horrible engrish from my prefecture's police website, the other concerns various administrative documents.