I'd translate it as: "As for now, it's impossible to imagine living without the internet." You can see 은/는 as 'as for' or 'talking of' - we always say the topic first - it can imply it was possible to imagine living without the internet *in the past*. For this reason, it can be taken as an invisible/subtle 'but, however'. 은/는 always combine with the noun. In '산다는', 는 is used to make 산다 into an adjective. 는 것 is, as Jae-Woo Kim says, a form that makes the gerund. As for now, it's impossible to imagine living without the internet. as for now 이제는 living without the internet 인터넷 없이 산다는 것 it's impossible to imagine 상상할 수 없습니다 What's impossible to imagine? Living without the internet. 을 is used to clarify what the object is.

1. The first one you'd got is right. 2. 이제는 is an adverb meaning now, which modifies the whole sentence. 인터넷 없이 산다는 것 is the topic of the sentence, "living without the Internet" >> now it's unimaginable to live without the Internet. 3. You can think of 산다는 것을 as a gerund meaning living in English. 산다,verb + 는것,ing +을,objective case Noun+ 을/를 > the objective + 은/는 > the nominative + 의 > the possissive