I would wait on deciding what breed it is until the wildlife rehab can take a look to be sure. If indeed it isn't considered a wild bird, then you just take it back with you. If it is, then they'll take care of it.
No, you can't house doves with chickens. The chickens for one could kill a dove, and two, they could spread germs between them that neither is immune to, causing illnesses.
The age of these birds is fledgling, meaning, around two weeks old, they were most likely pushed out of the nest by their mother, who would have continued to care for them. This also means they are beyond getting crop milk and the parents would have transitioned them to seeds. You can get something
like this for it if you find it's a domestic bird and you're going to continue to raise it.