Your first example is actually borderline reflexive; we call these verbs "pronominal" when they require a reflexive pronoun (which for the third person is se) while the action is not truly reflexive. You can tell this isn't reflexive because we never say se levanta a sí mismo de la cama; the verb levantarse is not understood as reflexive. A truly reflexive usage would be e.g. se miró [a sí mismo] en el espejo ("he looked at himself in the mirror"). This is a fine point, though; syntactically the result is the same.
(In case you were wondering, we do say se levanta por sí mismo de la cama; the preposition changes everything. Instead of por sí mismo one can say por sus propios medios. In every case it means "by his own means/strength, without help". It's not reflexive.)
Some really non-reflexive verbs also employ this pattern, like caerse (you can tell they're non-reflexive because they're intransitive; a verb that can only take a subject and no object can of course never be reflexive). These are also termed "pronominal" verbs.
Your example about "impersonal se" is grammatically wrong; this is not impersonal, but the so-called pasiva refleja (reflexive passive) construction, which requires agreement between the verb and the subject: se encuentran muchos carros en la carretera a esta hora. The literal translation would be either "many cars are found..." or "many cars find themselves...".
Impersonal sentences always have the verb in the third person singular, and they're often difficult to distinguish from the reflexive passives. There are tests that you can do to decide which one is it. If there's a subject, by definition it's not impersonal. See this question and its accepted answer for details.