Learn Hardcore German: Die Chefin gab mir sofort eine freundliche Rückmeldung und ihre Zustimmung. - The female boss immediately gave me friendly feedback and her approval.

Yes. Chef is the masculine noun for boss; its regular feminine form is Chefin (base word + the feminine suffix -in). Because the subject is a woman, the nominative article is die: Die Chefin. Plurals: masculine plural die Chefs, feminine plural die Chefinnen. In everyday talk, die Chefin often simply means “my boss (who is female).”

Why is gab used instead of hat gegeben?

Both are correct past tenses of geben.

gab = preterite (simple past). Common in written German and narratives.
hat gegeben = present perfect. Dominant in speech. You could say: Die Chefin hat mir sofort … gegeben with no change in meaning or nuance beyond register.

Why mir and not mich?

Because geben governs a dative recipient and an accusative thing:

jemanden (Dative) etwas (Accusative) geben Here, mir is dative “to me.” mich is accusative and would be wrong for a recipient.

What cases are eine freundliche Rückmeldung and ihre Zustimmung?

Both are direct objects in the accusative. Pattern: Subject (NOM) + gab + Recipient (DAT) + Thing(s) given (ACC).

mir = dative recipient
eine freundliche Rückmeldung = accusative thing
ihre Zustimmung = accusative thing

Why do freundliche and ihre end in -e here?

Attributive endings:

With a feminine singular noun in the accusative (and nominative), adjectives and possessives typically take -e. So: eine freundliche Rückmeldung, ihre Zustimmung. The endings signal gender/number/case together with the determiners eine and ihre.

Can I use Feedback instead of Rückmeldung?

Yes, many people do. Nuances and usage:

Rückmeldung (f.) = native, neutral style; very common: eine Rückmeldung geben/erhalten.
Feedback (n.) = widespread in business/tech; you’ll hear Feedback geben a lot. Singular mass use is common; plural Feedbacks exists but some style guides prefer avoiding it in favor of plural Rückmeldungen. If you want a slightly more formal or German-sounding option, choose Rückmeldung.

Does freundlich imply the feedback was positive?

Not necessarily. freundlich describes the manner/tone (polite, kind), not the evaluation. You can get a friendly but critical Rückmeldung. For a positive evaluation, you’d say positive or lobende Rückmeldung.

What’s the difference between Zustimmung, Einverständnis, Genehmigung, and Einwilligung?

Zustimmung: approval/assent; you give your OK to a proposal/plan. Collocation: jemandem seine Zustimmung geben.
Einverständnis: agreement/consent; emphasizes mutual understanding or being on board.
Genehmigung: official authorization by an authority (permits, bureaucracy).
Einwilligung: consent in a legal/personal-rights sense (medical procedures, data protection). In this sentence, Zustimmung fits best.

Why ihre Zustimmung and not Ihre Zustimmung? Could ihre mean “their”?

ihre (lowercase) = “her” (or “their,” depending on context). Here it refers back to die Chefin, so it means “her.”
Ihre (uppercase) = formal “your.” Because it’s mid-sentence and refers to the subject, ihre must be lowercase and means “her.”

Why is there no comma before und?

Because und is joining two coordinated objects (eine … Rückmeldung and ihre Zustimmung). German doesn’t use a comma to join simple parallel elements. You’d use a comma if und connects full clauses with their own verbs, or for certain parenthetical structures.

Do I need to repeat the verb or dative, like gab mir … und gab mir …?

No. The single gab mir governs both coordinated objects. Repetition is only for emphasis or clarity in long sentences. The original is concise and natural.

Can sofort be placed elsewhere? Is sofort mir acceptable?

Neutral: Die Chefin gab mir sofort … (very natural).
End-focus: Die Chefin gab mir … sofort (emphasizes immediacy).
Fronted for strong emphasis: Sofort gab die Chefin mir … The variant Die Chefin gab sofort mir … is generally avoided because short pronouns like mir tend to stand earlier than adverbs in the middle field.

What’s the difference between sofort and gleich?

sofort = immediately, right away (unambiguous).
gleich = very soon/in a moment; in some regions it can mean “right now,” but it’s more elastic and can sound less immediate. If you need to be crystal clear, prefer sofort.

How do the plurals work for Rückmeldung and Zustimmung?

Rückmeldung → Rückmeldungen (common).
Zustimmung → Zustimmungen exists but is rarer; often used when counting approvals (e.g., votes). Otherwise Zustimmung behaves like a mass noun: viel Zustimmung.

Why are Rückmeldung and Zustimmung capitalized but freundlich is not?

All nouns in German are capitalized: Rückmeldung, Zustimmung, Chefin. Adjectives like freundlich are lowercase unless they are nominalized (used as nouns).

What exactly is gab? Can you show the key forms of geben?

gab is the 3rd person singular preterite of geben.

Present: ich gebe, du gibst, er/sie/es gibt
Preterite: ich gab, er/sie/es gab
Past participle: gegeben
Perfect: er/sie hat gegeben

Why use ihre Zustimmung rather than die Zustimmung?

With Zustimmung, German strongly prefers the possessive to mark whose approval it is: jemandem seine/ihre Zustimmung geben. die Zustimmung would sound generic; ihre ties it clearly to the boss.

Could I rephrase with other verbs, like erteilen or mitteilen?

Yes, depending on nuance:

Zustimmung erteilen (quite formal/official): Die Chefin erteilte mir ihre Zustimmung.
For feedback/information: eine Rückmeldung geben/erteilen, or mir etwas mitteilen (“to inform me of something”).
You can also verbalize approval: Sie stimmte zu (“she agreed/approved”).

Is Chefin ever spelled Cheffin? Why only one f?

It’s always Chefin with one f. The feminine is formed by adding -in to Chef, without doubling the consonant. Cheffin is a common misspelling.