What's the difference between:
(1) te avisarei
(3) avisarei-te (if this is even correct?)
Are they interchangable?
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Avisarei-te is nonstandard; otherwise, all three mean the same. The choice between avisar-te-ei and te avisarei has to do with syntax and the presence of adverbs. For instance, in a simple main clause I would say:
Fica descansado, eu avisar-te-ei quando ele chegar
but in a subordinate clause (all in boldface),
Fica descansado, eu já disse que te avisarei quando ele chegar
This is so in European Portuguese and (very?) formal Brazilian Portuguese. In colloquial Brazilian Portuguese, the pronoun comes before the verb nearly all the time. See this question about the placement of these pronouns.
The distribution between avisar-te-ei and te avisarei is the same as between aviso-te and te aviso. The reason we have the pronoun in the middle of the verb rather than at the end is that the -ei is a remnant of the auxiliary verb haver (same with ia in avisar-te-ia); so a long time ago the te would be at the end of the main verb (avisar-te hei) just as in aviso-te.
In practice, you won’t hear avisar-te-ei that much (or te avisarei, for that matter), because we tend to replace the simple future with the present or ir + infinitive. Say, rather than the examples above, I would much more likely say:
Fica descansado, eu aviso-te quando ele chegar
Fica descansado, eu já disse que te aviso quando ele chegar