Restore my Mac from a Time Machine backup on my Time Capsule I don't use the wifi or router options of my Time Capsule, I only use its Ethernet. Do I need to activate the wifi in order to perform a restore? Thanks
No you don’t. It will work fine if you plug in Ethernet to any port except the wan port no matter what the settings. 

You could reset the time capsule if you want to be sure it’s in normal order and then the password will be known so you can reset it if needed to use the WAN port or otherwise look at the settings or know the passwords to the disk and management level.