Question

During this phase,the person becomes infected and the virus is active. It is attacking T-cells and slowly weakening immune system. The infected person feels well and healthy.

Answer 1

According to this, this is HIV (Yes?)
All people with this virus will not feel all symptoms, or anything at all.
Since this is slowly weakining the immune systems, the affects of the virus will not be considered until you really start to see it.
T-cells help the white blood cells, and white blood cells fight viruses, so the HIV will enter the immune systems, but all symptoms will not be applied immediately.