You can't just sing out loud whenever you like, other people live here too. I think it's better to say 这里还有其他人, 你不能想唱歌就唱歌. 胡乱地唱歌 means that one sings not according to either the words or the melody of the song but at will or at random. Whenever refers to a condition/a situation, while 胡乱 is an adverb which describes 唱歌. Both your English and Chinese sentences are correct, however, they cannot be translated into each other.

这句话是可以的。胡乱 means something is disorder，doing something without thinking ，For example“those books are disorderly”这些书胡乱放着。

Do whatever you like. If you are happy.你开心就好。

胡乱 是 do whatever you want to do at your mood regardless of others' feelings or comment

“胡乱”在中文的语境里一般是指：不管不顾，不分时间，地点，场合，任意妄为地去做一件事。所以在你造的句子里是可以说得过去的，所以这里的“......can't......whenever you like......"就可以引申为”胡乱。这样解释，会明白一些吗？