Can I use the Eco-wifi together with my wifi booster?

A wifi booster is problematic in terms of electromagnetic (EM) radiation emissions. Basically a booster is a combination of a wifi receiver and access point. Therefore it emits the same level of EM radiation as an ordinary access point, which is what you are trying to reduce in the first place. Also a small number of lower quality boosters have problems with the reduced pulse interval of the Eco-wifi router. It is much better to pull a LAN cable to the point where the booster is and install a 2nd Eco-wifi router there.