Trying to translate: "By next week I will have recovered for sure" (meaning recovered from sickness) Have got out my grammar books and my "Deutsche Grammatik" (Helbig / Buscha) seems to suggest that the following translation would be grammatically correct:
Bis nächste Woche werde ich mich bestimmt erholt haben.
but I would like to know if a native speaker would really say this or prefer a different phrase.
There are three ways to express that.
Futur I (werden + [verb], that is) is the equivalent part to the English will-future when you want to express probability or an assumption.
Nächste Woche werde ich wieder gesund sein.
Futur II (werden + past-participle + auxiliary, that is) is the equivalent part to the English Future Perfect tense when you want to express an assumption about something in the past of a future time.
Bis nächste Woche werde ich mich erholt haben.
If you'd like to translate the sentence most closely to the English pattern, use this one.
Germans are not that accurate with tenses, though. Textbooks won't teach you this point (i.e. the inaccuracy).
According to them, we use present tense for facts and appointments in the future (like English: "The bus arrives at 6 PM" – "Der Bus kommt um 18 Uhr").1
And though, we tend to use the present tense even for assumptions.
Nächste Woche bin ich wieder fit.
To indicate that it is an assumption or that is very likely, we add words like bestimmt or mit Sicherheit, respectively. On a side note: You don't really need these words in the first two cases above (i.e. Futur I and Futur II) since they're used for assumptions per definition, but it's not unlikely to do so, though.
Nächste Woche bin ich bestimmt wieder fit.
Nächste Woche bin ich mit Sicherheit wieder fit.
If you'd like to translate your sentences in a way as a German would've said it in the first place, use this one.
1 Naturally, there are more use cases of present tense but I focus on future in this answer.
Your answer is fine.
More colloquial, but shorter, you could say:
Nächste Woche bin ich wieder fit
or, to leave some room for uncertainty:
Nächste Woche bin ich bestimmt wieder fit
where the bestimmt indicates an expectation as opposed to a fact. You could of course replace fit with gesund.
You would most likely use fit if currently you are not really ill but just feel a bit under the weather, maybe have a cold, where gesund as opposite of krank indicates a somewhat worse current state.
This is fine detail, though, and depends a lot on personal preferences, with fit being quite informal.
I would say 'Nächste Woche bin ich (ganz) sicher / bestimmt wieder gesund' - but your sentence would not sound so weird to me, either, maybe a little bit too long. The 'ganz' puts emphasis on the level of certainty, like 'for sure' does, so if you want to express that you will definitely be healthy by next week, use the 'ganz'.
A problem is, that the German equivalents to "recover" in health context (which would be "genesen" or "gesunden") sound awfully dated are not really used. In conversation also the correct future tense is somewhat disposable. "Erholen" is the best match, but would also apply to recovery after hard work, sports or similar.
Some proposals on colloquial level:
