grammar - What do で and ように express here?

For full context: http://www3.nhk.or.jp/news/easy/k10011221251000/k10011221251000.html

The sentence in question:

ＪＲ東日本は、新幹線で無線のＬＡＮのサービスを始めて、無料でインターネットが利用できるようにすることにしました

My problems are the parts in bold. First, my attempt at translation:

JR-East-Japan has decided that, establishing wireless LAN service in shinkansen, they make it so that you can use the internet for free.

So, first there 新幹線で and 無料で. In the way I translated these parts, it feels like I'm wrong. Whenever で is a particle that marks a location, it usually was in context of an action happening in this place. In this case, "establishing WLAN" can be interpreted as an action happening there, however, the cases I used to encounter with で expressing the semantics I mentioned above were more of this sort: キャシーがパーティーでなに何をき着ていたかおぼ覚えていますか。 And I think that this is something else, although I could be wrong as well of course.

Second, 無料で. It's a similar problem here. I interpreted 無料で as 無料 + conjunctive form of だ. In this case, the literal translation would be:

...being for free, they can use the internet.

However, this already expresses something else than what I translated above, I think. I can't think of another way to translate this meaningfully, and it fits into the context very well.

Third, ように in インターネットが利用できるようにすることにしました. I translated it in a final sense like in "They do X, so that they achieve Y." However, combined with することにしました it sounds rather overcomplicated to me: "They decided that they do, so that X/in order to X...". That's why I feel the need to ask for confirmation...^^ I also know a different meaning for verb+ように, which would be something along these lines: 学生に図書館で物を食べないように注意しました。 Here, my textbook says that "this structure is used to quote the contents of an order or request.". Since sometimes the definitions turned out be defined too narrow, I wanted to bring this up in context of this question.