Can I get this angle ??

Question

Step number (1) is correct or not?

and if correct can I get angle AEB?

Answer 1

Note that line $EF$ can be moved left and right without altering any of the given conditions. And doing this clearly changes $\angle AEB$. Thus the information provided is insufficient.

On your approach, it is not correct because on adding that area, one triangle is right angled whereas other is obtuse.