What does the sentence 该视频随即被上传至网络，转发量过万 translate to?
Considering the context of the article, I would translate this as:


  该....视频.................随即.........被上传....至....网络，......转发量...过万
  the video (was) immediately uploaded to the internet (and) the number of shares/retweets/reposts (is) over 10k


该 indeed means "the above-mentioned" but in most contexts you can just translate is as "the". In normal spoken conversation we'd say 这个/那个.

被 is a passive marker, indicating that the subject is the receiver of the verb rather than the do-er, i.e. the video did not "upload", rather it "was uploaded".

至 just means 到 (to). It's the formal character, common in news etc, but in normal conversation we would say 到.

The character 量 means "quantity" and can be added after a noun. For example "转发" is "forward/share/retweet" and "转发量" is "the number of forwards/shares/retweets".

过万 simply means "over 10000".