Delta says they require a health certificate when you talk with them on the telephone. At the counter they have never asked for one from me. The last time I was at the Delta freight office there was a notice on the wall saying the animal must have an acclimation certificate if the temperatures are going to be below 45 degrees. Maybe that is the health certificate they are talking about. Regarding the carrier, use care and common sense.
Some carriers come with dishes.
When using a carrier without a dish, I have glued a plastic dish to the bottom of the carrier or to a large piece of cardboard so that it cannot be tipped over. I provide lots of fruit rather than water, which can spill or dry up. Most birds prefer a perch and most carriers do not come with them. I have fitted perches in the carrier myself to make the bird more comfortable or have allowed them to perch on the edge of the dish. Newspaper is a common substrate or you could use a rag, towel, or old T-shirt as long as there are no frayed edges for the bird to get tangled in and as long as the bird is not a chewer.