About 90% of all the species that have ever lived are now extinct.
That’s just an estimate, of course. We don’t even know for sure how many species of animals there are today. What we do know is that in the 500 or 600 million years that animals have been around, a lot of species have gone extinct.
There’s a good graph of marine animal families at this site. When the line goes down, that means that entire animal families have gone extinct. The families here are not like households, they are the taxonomic group between genus and order. For example, all cats—house cats to lions—belong to the family Felidae.
To answer the other part of your question. We share DNA with all animals. We just share more DNA with our closest relatives. A lion shares more DNA with a tiger than it does with an extinct saber-toothed tiger. All species evolved from species in the past. We all inherit our DNA from our ancestors. Sometimes a mutation happens, changing the DNA. As these differences accumulate, two populations can become so different that they can’t interbreed anymore. When this happens, they are different species. They still have a lot of DNA in common though. We have a lot of DNA in common with flies and dinosaurs, but a lot of it is also different.
A good way to research the information would be to search for: evolutionary history of... (whatever species interest you). For example, I chose evolutionary history of whales and found a great page that shows extinct species related to modern whales: here. The diagram shows groups that are still alive (toothed whales, baleen whales, and hippos), as well as extinct animals.
The process of species splitting off can take a long time. Even when species look different, they may still be able to interbreed if they are brought together. The result is a hybrid. Can you think of any animals that are the result of crossing two different species? The species have to be closely related, of course.
Thanks for asking,