There has been many many experiments where they take Stem Cell and replace the DNA, or change the DNA. Transgenic mice are the most studied. https://www.criver.com/products-services/research-models-ser...

There have been succesfull experiments with xeno-pregnancies aka interspecific pregnancy. https://en.wikipedia.org/wiki/Interspecific_pregnancy#:~:tex....

With current technology, we very much do indeed experiment with DNA of animals.

As for making DNA from raw materials, that is what DNA printers to. see https://en.wikipedia.org/wiki/Artificial_gene_synthesis