As if they were all suffering from a sleepless night, or almost done recovering from a broken nose. 

or 是并列连词，后面的成分不完整，是因为承前省略了相同的成分：or they were。

补充完整为：

As if they were all suffering from a sleepless night, or they were almost done recovering from a broken nose. 

【翻译】好像他们都经历了一个不眠之夜，或者是他们的鼻子骨折了尚未恢复的样子。

done 是形容词（完成了；做完了），almost done 指“人做事情几乎快完成——实际还没完成”。后面的recovering from a broken nose 是done 的方面状语。意思是“鼻子骨折了，塌陷了，还没恢复过来”。