Can one computer/server have two hosts/participants?
Yes, one server can host many participants, each at 64GB (revised from the original 8GB). It's expected that most servers will have on the order of dozens of participants, and we're trying to write the program such that a modest machine (maybe $300) can handle all of the computational power required to operate ~20-50 TB. These are all vague estimates at this point.
For a quorum, is it true that the only time for a quorum to be down is the time that the quorum loses all 28 redundancies and one or more of the other 100 participants are down? How does a quorum or host get recovered from catastrophes?
So, this has a lot of answers. Quorum-important data like error-detection and wallet info, as well as the block history is either stored at full redundancy (everyone in the quorum has a full copy) or at a redundancy of 8. So wallet data and other equally important data will only be lost if 112 out of 128 participants go offline at the same time. This gives us extremely high reliability, even when the assumption is that 50% of the network is dishonest.
Files on the other hand get to choose their redundancy. If you are storing extremely important documents (like your private keys, for example), you'll want to choose the maximum grade redundancy. This comes at a cost, instead of paying $5 per TB per month, you'll be paying $50 per TB per month. But if you're only storing 100kb at that price, who cares? For everyday files, you'll want to pick a more reasonable redundancy, like 100 out of 128, which means that your file will only be lost if 28 participants disappear at the same time. Assuming no malice and reasonable uptime (like 98%) per participant, it's extremely unlikely that you'd lose the file. We let users pick their redundancy because everyone is going to have different levels of paranoia/trust in the system, and we don't want to force one person to pay what they consider to be 10% too much and force another person to have redundancy that they worry is too little.
When one or more participants go offline, the network immediately replaces them with new participants. This involves having the new participants download the files and error-correct them and consumes a lot of bandwidth. This can be optimized in a few ways and we're exploring the best way to handle this. Overall, replacing a lost participant should take something in the 6-8hr range, and even less if the new guy has lots of bandwidth. That's why we set the default at 100 non-redunant participants. Assuming 98% uptime, it's going to be extremely rare that 28 out of 128 go offline in the same 8 hour window.
If the network is malicious though, and 50% of participants are cooperating to take down a file, they can all go offline together and a 99.9% uptime wouldn't save the file. If you're paranoid about your file being attacked, you should use the 8 redundancy that the network as a whole uses. (16 non-redundant participants)