Your first consideration:
In place of: "Apago las luces," we may make the verb reflexive of its subject and say: "Las luces se apagan" in order to emphasize the object instead of the subject.
is not accurate.
Although the passive voice can be formed with the particle "se," the passive meaning is not always present when "se" is there. In fact, apagarse can be understood as a pronominal verb used to indicate that the action takes place without the necessary participation of an agent (perhaps the lights go out automatically when the day breaks, or because there is a blackout, and not necessarily because somebody turns them off).
"sentirse" and "referirse" are clearly pronominal. Now, your sentences:
(1) *Para estar alegre, se necesita sentirse seguro.
(2) *Para estar alegre, se necesita sentir seguro.
are ungrammatical because you cannot use a pronominal verb after an impersonal one (sentence 1 above) and because "sentirse" needs to be pronominal to make sense in this case (sentence 2 above), so some other alternative has to be found if you want to do away with "uno" and make the sentence impersonal:
Para estar alegre, es necesario sentirse seguro.
Para estar alegre, se necesita sentir seguridad. (less idiomatic, less natural than the former, but equally correct)
In the book "Valores gramaticales de se" by Leonardo Gómez Torrego we can find this interesting reference to the coexistence of two pronominal verbs:

We can observe that this phenomenon is possible because both verbs, the finite and the nonfinite one, share the same subject. Another case in which this coexistence of pronominal verbs is possible occurs when one of them is passive and an indirect object (which functions as the tacit subject of the infinitive) is implicit:
- Se recomienda quedarse sentado. (Staying seated is recommended.)
(This can also be understood as: Se recomienda a la gente quedarse sentada, where "la gente" is the subject of "quedarse sentada").
However, it is ungrammatical to have two pronominal verbs in a sequence when the first one (A) is impersonal or (B) is in a passive form that does not allow for a tacit indirect object:
(A)
- *Se necesita quedarse sentado. (incorrect)
- *Se puede quedarse parado. (incorrect)
- *Se debe quedarse quieto. (incorrect)
Instead, one has to say:
- Es necesario quedarse sentado / Uno tiene que quedarse sentado.
- Es posible quedarse parado / Uno puede quedarse parado.
- Es obligatorio quedarse quieto / Uno debe quedarse quieto.
(B)
- *Se abolió vestirse de luto. (incorrect)
BUT:
- Se prohibió (a la gente) vestirse de luto. (correct)
- Se autorizó (a la gente) vestirse de luto. (correct)
- Se exige (a la gente) vestirse de luto. (correct)
- Se permite (a la gente) vestirse de luto. (correct)
- Se requiere (a la gente) vestirse de luto. (correct)