About your question "But why " Fa ginnastica." ? (Because to do a exercise must by myself?)"
The reason "fare ginnastica" is not a reflexive verb is that:
1) the direct object of 'fare' is taken ('ginnastica'), therefore a direct reflexive verb isn't possible, because Italian doesn't comprise double direct object constructions ("* mi faccio ginnastica", where 'mi' would be the direct object as in "mi lavo": )
2) we don't say "fare ginnastica a qualcuno", therefore an indirect reflexive verb isn't possible either ("* mi faccio ginnastica", where 'mi' would be the indirect object, as in "mi lavo i denti").
Maybe you're confused, because the answers you received led you to think that we always use a reflexive verb when we do something which concerns ourselves. This is not the case.
For a reflexive form of a verb to exist, I'd say that, with reference to the relevant meaning of the verb, two conditions must be satisfied::
– the meaning is transitive
– the subject of the verb can also be its direct object (direct reflexive verbs, eg "mi lavo") or its indirect object (indirect reflexive verbs, eg "mi lavo le mani").
In other words, a reflexive verb is nothing more than a specific scenario in the overall usage of a transitive verb, namely the one in which the subject is also either the direct object or the indirect object: when this happens, the personal pronoun expressing that object is chosen in the reflexive series, that's to say mi/ti/si/ci/vi/si. That's all. :-)
One last thing. The meaning of the verb (the meaning you are interested in, if there is more than one) must be compatible with the double role of the subject, and I'm under the impression that usage plays a role here. For example, we say "Interpreterò Amleto" ("I will play Hamlet"), but, with this meaning, usually we say "interpreterò me stesso" instead of "mi interpreterò".
All I wrote goes for reciprocal verbs, too.