DECT phone do comes with either RJ11 (regular old phone) or RJ45 (Ethernet) plug. However, the phone and Internet are different signalling. It also has different voltage swing. Devices used for Ethernet signalling will not work for DECT phone that reason, I believe.

aneip suggestion is very good idea. Normally for 2-story house, there are 2 separate phone wires. One to ground floor and one to upper floor. These wires go one point at the edge of the roof for external phone line connection. If you join these two wires, you have connection between ground and upper floor. You have parallel phone wire pairs.

In fact most phone wires has two pairs of wire, even though only one pair is used by phone. These two pairs can be used as Ethernet cable. I believe it is still good even for 100Mbps. Just need to replace with RJ45 connector to it.

If you still want to utilize your house wireless LAN (well if wireless LAN can cover the whole house, there is no reason the DECT can't cover, I think  ), you can use this device, which I found the least expensive so far:

http://blog.thetelecomspot.com/how-to-exte...sipvoip-fxofxs/

I think you just need to plug the HT-503 to your wall phone socket and then plug the LAN cable to your wireless router. On the receiving end of the LAN, you need the HT-502 that will act as your FXS point. I hope I understood the device correctly 

installed the sonoff switch, working nicely; put some foam tape behind pcb to prevent shorts;

now, 3 ways to open gate 

can you tell me yellow and black cable go to which port in autogate board?

The yellow and black cable go into your signal port to open and close the gate.

from COM/NO to COM/2S