How to say: "After cartoons are over" or "After she's done watching cartoons" or how?
Solution 1:
Any of the three would do, except that the third would be better as
"I'll read stories to her after the cartoons."
That said, it's probably the least satisfactory of your three options anyway.
To throw another alternative into the mix:
"I’ll read stories to her once the cartoons are over."
Solution 2:
"I'll read stories to her after she's finished watching cartoons."
Solution 3:
"I'll read stories to her as soon as she's done watching cartoons"
is acceptable but is much more American English in style.