Good questions.
The DTube and DLive tags are stored in the blockchain, and can be used easily. The original YouTube video tags are collected into our database, but I'm not yet sure whether to use them or the Steem post tags (or both) for searching/filtering.
Currently the hot/trending scoring is based (similarly to Steem), on a combination of the pending payout and the time since the video was created, there is no connection to the YouTube voting at the moment. I'm free to try a different formula because I'm using a separate database, but it needs to be quite efficient to calculate since it must be done frequently (so looking up YouTube votes every few minutes probably won't work), but it's an interesting thought.