MongoDB supports 1) 2) 6) 7). Not sure what 3 and 4 is, but you can just add a new node and new data will be copied over, no need to restore data from snapshot, but you can restore from snapshot too, it shorten the time the replice become available.

Not sure what you mean by 5) though.

Anyway, replciation is strong point of MongoDB with oplog and I don't think Postgres can beat it.