If I have nameservers with host #1, and host #1 goes down, if it also points to host #2 (like nameservers 3 and 4), will it automatically start using host #2?
It will, but there will be a delay as the resolver's query has to time out first. By that I mean that every client that visits your site and their resolver chooses host #1 will experience a delay before host #2 is queried
It's possible, but not in the way you describe. If you use the nameservers from two providers then they must both provide the same information, which means having all nameservers direct traffic to one or the other server (or both). Google "failover dns" and "round robin" for more.