After Vala explains that she wears the Super-soldier suit which absorbs energy weapons, Daniel retorts that he's aiming the Zat at her head. A fight scene ensues at the end of which Vala, while still wearing the protective suit, receives a Zat blast (at around 17 mins) in the thigh, knocking her out. She wasn't wearing the outer armor, so she wasn't actually protected. In addition, Vala is deceitful, so she may have been lying about it as well.
When General Hammond gets kicked off the Prometheus by Vala, he refers to it as his "ship". Being an Air Force General, he would more likely refer to the Prometheus as his "craft" or "spacecraft". In the present day, real examples are called 'spacecraft'. However, he and other characters would have grown up with much larger, fictional vessels (e.g., in Star Trek or Star Wars) being referred to as 'ships' or 'spaceships', so the usage is understandable.
Vala says the moon where her people took refuge didn't have a stargate. People who had no contact with Earth or the Tau'ri would not know the word "stargate" and would call it a "chappa'ai".