In this case hado is "hard" (ハード) and just means spicy, as does 辛口 (karakuchi) written next to it in brackets in the manga. Karakuchi can mean "salty" but with curry it's referring to the level of spiciness. (See here on the packet.)
Zaasai translates to "Szechuan pickles." Here is an example of "zaasai namuru."