After I installed another Omni Lamp mod this one showed up as well.

The Omni light no longer shows up in the crafting menu, you can only craft the Tek lamp. I've set it to the top of the mods and still nothing.

I have no option to turn it on and it doesn't turn on when its dark, what am i missing?

It takes 3 omni lamps to craft 1 powered one and 2 tek lamp to craft 1 powered one

So if you type in powered in the engrams you will find them i dont remember exactly what level you learn them at but you need to know the omni lamp to learn the the powered one and you need to know the tek lamp to learn the powered one. After you have learned them in the crafting section in your inventory just type in powered to craft them in your inventory

how do i learn this in the game. i cant find it in any inventory

Yeah no fuel is needed you just make it, place it, and turn it on.

Does "self-powered" mean it requires no fuel, or that it takes fuel instead of electricity? I presume the former, as the latter would be ... underwhelming :)

Everything should be all good now

Sorry people just off work and i noticed the tek lamp not placing properly im working on that now sorry for any inconvenience