Yes: RTFM. The "small" unit does not broadcast WiFi because it doesn't. Your WiFi kit contains one plain PLC adapter to be used near the router, and one PLC with integrated WLAN access point to be...

Heh. Well recycled.

No it wouldn't - the original HomePlug standard at 80 Mbit/s is not compatible with anything that came after it. [All the newer stuff does retain full compatibility, all the way from 200 to 2000...

If that's not it, your router may have a poorly designed power brick that allows the PLC "noise" to strike through to the router's internal electronics. Try a powerstrip with an integrated filter, or...

This happens when your house wiring runs the (possibly unshielded) phone wire in the same wall pipes as power wires. Since DSL and PLC use the same frequency range, power wiring is never shielded,...

Indeed ... check whether that cable you used on the router is actually a 4-pair (8-wire) cable, not a simple 2-pair 100 Mbit/s cable. You can usually see that on the transparent connector bit.