In the first one, the “limp” is supposed to be the contact pose, that is the point where the skeleton transfers weight from the back foot to the front foot. Same with the second one.
As the wight shifts it causes a change in the speed at which the body drops towards the ground. When the leg is then braced, the shift stops. It should give an indication of the wight of the subject, if it’s done right. Not sure I’ve got the hang of it yet.
Your 4 legged animations are pretty good, If you want to learn more, search for traditional animation cartoon run cycles. There are some nice pencil and paper dog animations on youtube. Of course it all depends on what animal you want to model.
For a dinosaur, I’d recommend modeling it on a lizard. Only more upright (lizards spread their legs out to the side).