So you extract your .obj and .pc2 file from max to marvelous design and you make the animated cloth.
What I DON'T know is how to make something like that:
I want the female character GRAB with her hand the skirt I made in MD, and lift it up. How can I approach a solution for this?
Export the figure you're making the clothes for in the posed position. Make the clothes on the posed figure. Pin the part of the skirt she's grabbing to her hand. When you've finished pushing and pulling all the fabric the way you want it export port it as an obj.
In your rendering software pose the figure, import the clothing obj. Parent it to the figure and render. You won't be able to repose the figure with the same clothing but you can always just reapply the pattern to the default figure pose in MD and then make it a conforming cloth figure in your rendering software.