Typically, the Notice of Foreclosure is also referred to as the filing of the Lis Pendens. This filing happens when the lender starts the foreclosure process. In New Jersey, this process can take 9-13 months. Many lenders are backlogged, and there are several ways the homeowner can delay the process. Homeowner's in foreclosure can file extensions delaying the sherrif sale and/or file bankruptcy. You can check with your local sherrif's office (in many areas this information is also available on-line) to see if the home is scheduled for auction.
Your concerns about the number of pets may be addressed by your local municipality. Every town has different rules regarding pets.
I too have tried to break into the REO game. I have spent about $1000 and so far nothing.
I joined Equator, and paid for their Platinum certification. I joined a few directories and signed up with four asset management companies. I have concludes that most of the REO listings are going to a few brokers who have been in the REO business for a while and have well established relationships with the asset managers for the banks. Some bank asset managers assign one broker up to 100 listings at a time. In Orange county where I work we have two or three brokers getting most of the REO business! If you go on Equator and check listings you will see the same brokers/agents over and over. Some banks now claim to be trying to have listings assigned to agents closest to the property. I guess we have to wait and see if they apply this idea, and if so perhaps the door will open for some new REO agents.