Have different animals have babies then let those babies have babies with different animals.
No.
The olinguito
An international team of scientists says it has found a "lost world" in the Indonesian jungle that is home to dozens of new animal and plant species. ... its face - the first new bird species to be sighted on the island of New Guinea ... undescribed plant species, including five new species of palms ...
If the species is scientifically proven to be new or undiscovered, then the person who discovered it gains the right to name the new species. The scientists who study the species decide to add it to the new species list.
To make a long answer short, when a variation helps an animal survive in its habitat, that animal will become more successful than it used to be, and enough variation can lead to a new species.
yes of course they can they are discovering new weird and wonderful species all the time
If one animal has a mutation and breeds with another animal then a new species may arise. The gene of the mutation may be carried down in the babies.
Lions may be bred with Tigers to make two different species, although those species are rarely able to reproduce, although there have been some cases. A male lion and a female tiger will produce the hybrid animal - Liger. A male tiger and a female lion will produce the hybrid animal - Tigon.
There are only 240 or so primate species. That is nowhere near 98% of animal species. Somewhere between the 6 and 9 million insect species on Earth make up about 90% of animal species total.
New species are introduced into areas to either get rid of another animal e.g. the cane toad came to Australia to get rid of some kind of bug or and animal is accidentally taken to another country.
There are many more arthropods than other species but bacteria have the most species. Every new species of arthropods discovered have 10-12 new species of bacteria in them.
You should talk to an animal conservation and tell them about the new species and then decide if you should protect the new species or not.