Why Is My Dog Blowing Hard Out Of His Nose?

Sounds like he's got flu. I'd usually say something less sinister (like a bug has crawled up or dust has settled there, which has happened to my staffie, and he's trying to blow it out) but the loss of appetite is never a great sign. I'd take him for a check up.

He is trying to remove nasty gunk from his nose or he could just be trying to keep his nose moist.
(P.S. A moist nose tells you he is healthy, his his nose is dry, he is sick.)

H1 Cassandra, I consider your attitude towards your pet "Good"!
Now, since you know that the dog is being adopted try and find out the previous history of the dog before you see vet doctor to avoid unnecessary spending. Also try and make it eat something because it needs strength for day-to-day activities. Finally, show love to your pet may be thats what it wants.
Good luck