Many materials for learning Spanish, discuss the "impersonal se" (e.g. ¿Se puede tocar esto?) and "passive se" (e.g. Se habla español.).
What exactly are these forms grammatically? Is the se in both cases a reflexive pronoun, or is it playing a completely different role? What are the rules for combining an impersonal or passive se with other reflexive, indirect, or direct object pronouns?
First of all, the formerly named reflexive verbs are denominated now as pronominal verbs. About pronominal verbs, you can read this answer of mine. You are interested in the role played by the word se:
El pronombre reflexivo indica que la acción expresada por el verbo pasa, como complemento, al mismo sujeto que la realiza. Es decir, es una palabra que repite el grupo del sujeto, en función de complemento.
To learn the different combinations of pronominal verbs with another object pronouns, you should completely read "Los verbos pronominales" (long but interesting document). I hope you will see things more clearly.
About the difference between reflexive passive and impersonal sentences, this is one of the FAQ you can find at the RAE website.
La confusión entre las oraciones de pasiva refleja (con el verbo en tercera persona del singular o del plural, concertando con el sujeto paciente) y las oraciones impersonales (carentes de sujeto y con el verbo inmovilizado en tercera persona del singular) únicamente puede darse con verbos transitivos, pues son los únicos que pueden generar ambos tipos de oraciones: Se buscan casas con jardín (pasiva refleja) / Se busca a los culpables (impersonal).
It gives three ways to decide which is the kind of sentence. The only case to use the impersonal is this:
Si el elemento nominal expresa persona y va precedido de la preposición a, debe emplearse la construcción impersonal; por tanto, el verbo irá en singular aunque el elemento nominal sea plural:
Entre los gitanos se respeta mucho a los ancianos.
Se entrevistó a los candidatos para el puesto.
Se busca a quienes presenciaron lo ocurrido.
Related to this subject, you've got also entry "2. Se indicador de oraciones impersonales o de pasiva refleja" at the DPD.
Although the example in the question are impersonal se and not reflexive se, they do follow many of the same rules. The meanings are completely different, but look at these examples:
Spanish is spoken. Se habla español.
Spanish speaks itself. Se habla español. (Español se habla.)
The word order could go either way.
Cars are sold. Se venden coches.
Cars sell themselves. Se venden coches.
While they have completely different meanings, if you're trying to formulate an impersonal construction, it can be helpful for the verb agreement and structure to think of it (loosely) as a reflexive sentence.
From textbook rules, the impersonal se uses the same placement as the reflexive se. Se me rompió el brazo. My arm was broken. Impersonal se followed by indirect object pronoun. Once again, I find it helpful to form this sentence in my head as "The arm broke itself to me." It helps me to structure the sentence correctly even if this isn't actually reflexive. An example of the same pronoun order with reflexive se:
Se los pone. He puts them on. Reflexive se followed by direct object pronoun.
Now for what I've heard and read but not seen rules for:
No se puede tocarlos.
Impersonal se is split from the direct object los. I've never seen this done with a reflexive se that I can recall.
Please correct anything that I've missed or misstated.
se is not reflexive in neither example you gave, it's only reflexive when it can be translated to him-/her-/itself
For example: se miró al espejo : he looked himself on the mirror
edit: This isn't a golden rule, there are exceptions, like se ató los zapatos (he tied his shoelaces) which doesn't involve himself, but because although semantically the shoes are the object of the action, grammaticaly, in Spanish, the shoes are not who receive the action but rather the person tying them, hence se ató los zapatos instead of ató sus zapatos.
I guess a better way of expressing this would be: If the receiver of the action (most times the object of the verb) is the same as the subject of the action, then it's reflexive.
