Do these endometrial implants or endometriosis act like normal endometrium inside the uterus?

Not exactly. Although endometriosis tissue has the same components as the endometrium the behavior is different. Inside the uterus, the lining sheds itself monthly in an organized way. Endometriosis on the contrary, results in a festering inflammation that can cause pain, infertility and adhesions.
In Some ways. In some ways yes because they implants are sensitive to your body's own hormones production and they are more active at times when they are influenced by your hormones production.