In my corner of the U.S., examples #1 and #2 are very natural. However, the way we would express #3 is...
Does it cost anything?
If you need to use the verb "to charge," consider:
Will you charge me anything (for it)?
The reason I point this out is, in my locality, "charging" (a) is something that someone does for the sake of an aquisition, or (b) happens to an account or the symbol of an account (such as a credit card).
When you ask, "does it charge anything?" the subject is "it," but an "it" can't charge anything (it can be charged, but not do the charging). "It" is the reason for the charge. Implying that something else is being charged is complex because the relationship is important, so we expect to know who's being charged.
As I sit here and think about it, Example #3 is (for my locality) asking if "it" can make a charge, as if you were talking about your bicycle making a purchase at the grocery store.
Remember, that's a location-dependent observation.
You will find examples of anthropomorphization (where an "it" can do something) with some issues. The most common example is the issue of gun ownership in the U.S. It's common to hear the refrain, "guns kill." Obviously, a gun, sitting on a table, can't kill anyone without someone or something being done to or with the gun. (The common counter-refrain is, "guns don't kill, people kill"). I bring this up as an example of when you can find "it" doing something that, normally, "it" wouldn't or couldn't do.
English, there's always an exception.