It depends on your interpretation of rabbinic law. In most cases the answer would be no (since you're still causing the effect by your actions), but some frum families used to employ a shabbos goy [0] to light candles, do shopping, cook, etc. Any action is permissible if it was going to happen anyway, but you get into degrees of technicality of the definition of "what was going to happen anyway".

[0] http://en.wikipedia.org/wiki/Shabbos_goy

In general no. Non-Jews are not required to keep the Shabbat, but Jews can not ask them to do things for them.

There are two exceptions, one is in the case of urgency that is not life threatening (for example a cold baby in a house with the heat off). (If it was life threatening than you just do it yourself.)

The second is you can hint to the non-Jews. For example say: It's so dark in here. Then the non-Jew is doing it for himself and not for you, and it's permitted. However doing this is discouraged except when it's important.