This is a little tricky but I am going to explain it . 1 In English when you talk about an action in the past you use the past Here Americans of 1950 Enjoyed, 2 when you talk about an action that took place BEFORE an action in the past. Here 1949 ,1948 .... You use the PAST PERFECT. That is to have in the past + past participle Here had enjoyed The sentence should have been written Americans ....enjoyed......than had enjoyed Americans a hundred years before But to avoyed the repetition of the word enjoyed we just keep the. Had. Easy no ! (>. <)

Inversion in a subordinate clause is completely normal for formal writing. An advanced grammar book will explain more.

Yes, you said it. And in the constructions like ' other ... than', 'rather ... than' and 'different ... than' (American English for the last one), may also have ellipses after 'than'.

Thank you very much. So, the inversion like this often occurs in the sentence including comparative degree?

Is it possible that the original is: As a result, Americans of 1950s enjoyed longer and healthier lives than had a hundred years before. Explanations: 1) 1950s 2) no the second "Americans" 3) it is not inversion, but ellipsis: when the clause following 'than' has the same subject as that of the preceding one, you may ommit it. 4）this sentence may also be phrased as: As a result, Americans of 1950s enjoyed longer and healthier lives than had Americans a hundred years before. and yes, it's an inversion. When the clasuse after than has a long subject and a short predicate (for example, a mere auxiliary, just as the sentence you've given), to avoid the impalence, you may put the short predicate before the subject, and so there is an inversion.