3d applications like 3ds Max,Maya,Blender do a lot of things very well but are limited in the scope of the available tools that one does require a lot of knowledge of how to make use of the available assets like Mixamo.
As a primer there is a huge difference between a TA and a game animator
In the case of Mixamo the rigging and animations are based on the tool sets available in Motionbuilder of being able to retarget animations from the Mixamo rig to any base rig that you wish through characterization and the addition of a control rig.
Since Mixamo uses Motionbuilder as the preferred application the available templates drag and drop with out any additional work.
I mention this as knowing where the data originated is rather important as to the question
“My question is, If you just get an animation from the site. Then a mesh.”
as by extension Mixamos animations can be retargeted to other templates I have on hand for the Epic rig and Genesis 3/8.
Looking ahead though I figure Epic is going in this direction as to the creation of the auto-rig as well as being able to retarget animations as you would only have to build a template.
Can any mesh be used with the animation?
Of course. The mesh used has little to do with function of a control rig with exclusion to morph targets or cluster shaping