I'll try to answer as best I can.

1. No way to stream to your DVR, it's live. To be able to watch it on your TV, you would need to either stream it on a laptop and hook your laptop up to your TV through an HDMI cable, or use something like a chromecast to do that wirelessly.
2. Yes, they do archive. But, you may need to be a premium member to watch archives, I'm not sure.
3. It is cheaper to buy all 6 days ($145) than individually ($30 a day). You basically get a day and some change for free.
4. I've bought the stream the last 4 years, I think. I would rate it a 4. There are inevitably going to be a few hiccups with roughly 44 hours of live racing being streamed (you may have to refresh the page a few times throughout the week if the stream freezes.) They have multiple camera shots, slow motion replays, interviews, live announcers. Back to back prices increases are a little hard to swallow, but I understand this year's with the added night. I will continue to purchase, however.