Yes ECE graduates are eligible to apply for the post of electrical engineer post in all government departments but they should clear the competitive exam held by the department.

Even in PWD many Electronics engineers are working as Electrical & Mechanical Junior Engineer . Subjects of ECE and Electrical engineering is almost the same but ECE has more complex subjects than electrical engineering.

No, ECE students can't apply for SSC JE. JE is basically for Electrical, Mechanical & Civil.