I can't place this gate anywhere. Only on the starting planet.
If first gate at starting planet, where I can/should place the second one?

In the settings there is only - Unknown key: "mod-setting-name.stargates-se-homeworlds-only". But turning this parameter ON or OFF does not give any results.

Thanks for catching this, not only was the localization for the string not working but the setting itself wasn't functioning correctly. It's fixed in the latest version (1.0.3), leaving it unchecked will allow you to place Stargates on any planet.

Now it can be placed, but it seems to me there is something wrong. Energy: 5.00Gj/1.00Gj
Is it right?

Yes, it takes 1GJ of energy to fire, but can store 5GJ of energy. I'm still tweaking the balance, might end up either lowering the buffer or raising the energy cost to fire.

When I click move to another planet

Error while running event stargates-se::on_gui_click (ID 1)
LuaEntity belongs to surface nauvis (index 1) but a LuaEntity belonging to surface Donn (index 6) was expected.
stack traceback:
[C]: in function 'draw_animation'
stargates-se/script/stargates.lua:537: in function 'activate'
stargates-se/script/stargates.lua:488: in function '?'
stargates-se/script/stargates.lua:624: in function 'handler'
core/lualib/event_handler.lua:47: in function <core/lualib/event_handler.lua:45>

That's one I haven't seen before, I'll have to dig into it.

A potential fix is up but I haven't been able to test it thoroughly yet.

Works without any problems! Thank you very much!

Thanks for your help!