No. No to this hippogriff.
1. An Eaqus resembles a mighty mustang but with the eyes, legs, tail, and appetites of a mighty eagle. It climbs and nests in trees, its bird eyes looking much more human, out from a slender horsey face. Its teeth are ill suited for its diet of meat and marrow, adept at breaking and mashing into paste but not tearing or rending. The talons help, but it still means the Eaqus must use its long, spiked tongue to loll and lick at the mash it makes of men. They are hurt particularly by blunt force damage, for their bones are hollow. They are fearsome in flight, using their powerful legs and light frame to leap tremendous distances (up to 240' wide and 120' high at a go each round) and their step and weight are preternaturally light. In this way they can run across the treetops, soaring over a forest pausing just long enough to snatch up a napping jaguar and ride it into the ground for lunch. They hunt and fly in herds, and their chicks hang onto their manes and tail, trailing behind in the wind.
2. Hyppoleon are...did you see Human Centipede? Or have it described to you and never actually watch it? Yeah I thought the second one. Well it's like that. It's like a big six-legged creature with a horse's ass, lion face, eagle middle, legs matched to the different segments, and six wings. It is all fucked up and flies like Chinese dragons. When it cries it does so with the voices of all three creatures. It spends a lot of time on the ground, running not-quite-in-sync with itself, effectively half-slithering half-running through the tall grasses and deserts. It has a love of fish, so it can also swim. This is how most people know them: with their legs hidden by the waves, they are often taken as sea serpents.
3. Half-Gryphons are winged lions the size of a large Clydesdale, with furry little tootsies which match his mane. Their wings are largely vestigial, as powerful as a gryphon's but nowhere near capable of lifting this massive frame. Many have their wings clipped and shaped for showing for this reason. A popular heraldry animal and common to royal zoos and arenas, they are the object of a long struggle to bring the creature to heel for riding purposes. After all, an unclipped Half-Gryphon's wings smash like war mallets, and they tower above even most warhorses. They are, however, impossible mounts without magic, and present the problem of sex vs. image: the more majestic figures are cut by the male, but the male is too lazy and of scavenger mentality for fierceness in battle. Whereas the females are truly terrifying in battle but are smaller and lack the luxuriously long, brushable mane. They are also hopelessly inbred and accustomed to life as a possession, so that they will not survive the age of man.
4. A normal sized eagle with a lion's tail and a horse's legs. Not proportionate to its body but like bad taxidermy. Wingless. Nature will not allow this creature to be. It lays one egg and then dies. The egg contains a proper gryphon. Until then, the hippogriff scavenges like a mongrel and eats the leaves from trees to quiet its angry belly. It lays its egg on the first black moon after it itself hatches. If this moon comes too soon, say before it has grown two weeks, it dies in the laying and the baby gryphon must scratch its way through not only shell but flesh to be born.