Do birds descend from dinosaurs?
First, it is confusing to say things like
- Birds descend from dinosaurs
- Humans descend from monkeys
- Mammals descend from vertebrates
- Snakes descend from animals
It is much more correct to say
- Birds are dinosaurs
- Humans are monkeys
- Mammals are vertebrates
- Snakes are animals
You should definitely have a look at the post If dinosaurs could have feathers, would they still be reptiles?.
Can we resurrect an ancestor from a modern day individual?
By looking at your genome, we can't know the entire genome of your mother. By looking at any modern day genome, you cannot fully know the genome of an ancestor. That being said, we can find DNA in pretty good conditions in fossils (ancient DNA aka. aDNA), so that there are ways to get to a pretty good aproximation of an ancient dinosaur genome without having to even consider the modern day descendents (or rather modern day most closely related lineages).
Can we resurrect an ancestor aDNA?
Bringing an extinct species back to life is called de-exctinction (or resurrection) and, if I am not mistaken, it has never been done. Candidate species for de-exctinction are species that are closely related with extant modern species so that we can use our knowledge of their biology and use the zygote of this extant species and just replace its genome. It is hard to imagine doing so with a species that disappeared in the Jurassic as it is already an important challenge with, more recently extinct species such as the wolly mammoth or the passenger pigeon.