1) Yep, looks right assuming you meant 16-18mA not 1.6-1.8. If you meant 1.7mA then you would have a resistor of 1800.
2) Not sure what you mean by "into a circuit with no components" but if you mean into 0v, then yes you'll get a dead short and BOOM
3 part 1) The button will register as low when you connect it to ground because ground IS low... the pin will be connected to 0v.
3 part 2) It's not the current that's really the point, it's the fact that it's connected to 5v which is what high is. You would get the same reading with no resistor, ie straight to 5v.... BUT and here's the important part, if you DID connect it straight to 5v with no resistor, when you push the button you'll be connecting that 5v straight through to 0v and BOOM
as you can verify by looking at this schematic