For some reason I can't breed anymore with my female dragon, puma, and my symurgh . Is there a breeding limit? Or I have to wait the next day to breed again. Thanks if you know. 

Your pets do have a breeding limit which varies on the pet's strength. This number is visible in the upper left corner of the pet's profile. But your pets do not seem to have hit that, and they still have full energy. 

It is my guess that you have reached your maxium limit that your stable can hold (remember creatures that are not born yet (ie pregnant critters). Double check your stable limit. You are at 19 pets, with one pregnant pet. You may need to construct a higher level stable (3 would be my guess), Let me know if you have questions on this and I can assist you :)

I would agree, most likely your stable is full. Checking your stable, you have 19 pets with one being Pregnant. Since the pregnant Puma counts double (mom plus baby), this means you have 20 actual pets, which is the limit for the level 1 Stable. Only thing to do is to increase its size by finding or buying a blueprint for Stable level 2, getting the materials needed and constructing it in the Manor -> Craft & Construction menu. 

That explains a lot. Thanks :)