1: If the cup has some devices and you broke it, then 「こわす」 is the right word. But, if it is an ordinary cup and you smashed it, then 「わる」 is the right one. 「わる」is used for fragile objects, like glass and crockery.
2: There are two reasons why "1" cannot be the answer. The first one is as 雲小泉-san explains above. And the latter one is a grammatical reason and the correct sentence should be 「そのころは大学 "に" はいっても、仕事がなかった」 instead of 「そのころは大学 "を" はいっても、しごとがなかった」.
3: じしょをひく is a set phrase as 雲小泉-san explains above.