Learn Hardcore German: Die Anfängerin ist noch unsicher, aber die Fortgeschrittene stärkt ihr Selbstvertrauen mit kleinen Komplimenten. - The female beginner is still uncertain, but the advanced learner strengthens her self-confidence with small compliments.

Anfänger is the masculine or generic form: der Anfänger = the (male / generic) beginner.
Anfängerin is the explicitly feminine form: die Anfängerin = the female beginner.

In German, many professions and roles have a feminine form with -in:

der Lehrer → die Lehrerin (teacher)
der Student → die Studentin (student)
der Anfänger → die Anfängerin (beginner)

So the sentence is clearly talking about a woman or girl as the beginner.

What exactly is die Fortgeschrittene? Is that a noun or an adjective?

Grammatically, fortgeschritten is originally an adjective meaning advanced.

In die Fortgeschrittene, that adjective is turned into a noun (a substantiviertes Adjektiv). German does this a lot:

der/die Reiche – the rich (person)
der/die Kranke – the sick (person)
der/die Fortgeschrittene – the advanced (learner / student)

Because it is used as a noun, it:

is capitalized: Fortgeschrittene
takes an article and adjective endings as if it were an adjective:
- die Fortgeschrittene (feminine singular, nominative)
- ein Fortgeschrittener (masculine singular, nominative)
- die Fortgeschrittenen (plural)

So die Fortgeschrittene here means the advanced (female learner).

Why do both Anfängerin and Fortgeschrittene use the article die?

Two reasons:

Gender & number
- die Anfängerin is feminine singular.
- die Fortgeschrittene is also feminine singular. So both are feminine singular, which normally takes die in the nominative.
Definiteness The die is the definite article: the beginner / the advanced one, not a beginner / an advanced one.
If you wanted indefinite forms, you’d say:
- eine Anfängerin
- eine Fortgeschrittene

What does noch mean in ist noch unsicher? Could I leave it out?

noch here means still:

Die Anfängerin ist noch unsicher
= The beginner is still insecure / unsure.

If you remove noch, it becomes a neutral description:

Die Anfängerin ist unsicher
= The beginner is insecure.

With noch, you imply:

She is insecure at this stage, but this may change later.
There is a contrast between her current state and a future (more confident) state.

You could also say immer noch unsicher for extra emphasis on “still”, but noch alone is very common and natural here.

Who does ihr refer to in stärkt ihr Selbstvertrauen?

ihr here is a possessive pronoun meaning her:

ihr Selbstvertrauen = her self-confidence.

Grammatically, ihr (her) could refer to either:

die Anfängerin (the beginner), or
die Fortgeschrittene (the advanced learner),

because both are feminine singular and there is no separate form.
So the sentence is slightly ambiguous in isolation.

Most likely interpretation from context:

Die Anfängerin ist noch unsicher → she lacks confidence.
die Fortgeschrittene stärkt ihr Selbstvertrauen → the advanced learner strengthens the beginner’s self-confidence with small compliments.

If you wanted to remove the ambiguity, you could say, for example:

… stärkt das Selbstvertrauen der Anfängerin …
(…strengthens the beginner’s self-confidence…)

Why is Selbstvertrauen written as one word and capitalized?

Two points:

One word
German loves compound nouns. Selbstvertrauen is a compound of:
- das Selbst (the self)
- das Vertrauen (the trust)
Together: das Selbstvertrauen = self-confidence / self-trust.
Capitalization
All nouns in German are capitalized, including compound nouns:
- das Haus
- die Tür
- das Selbstvertrauen

So Selbstvertrauen must be one word and capitalized.

Why is it mit kleinen Komplimenten and not mit kleine Komplimente?

This is about case and adjective endings.

The preposition mit always takes the dative case.
Komplimente is plural: die Komplimente (nominative plural).
In dative plural, with an article (or implied article), adjectives take -en:

(mit) kleinen Komplimenten

Compare:

Nominative plural:
kleine Komplimente sind nett. (small compliments are nice.)
Dative plural after mit:
Sie stärkt ihr Selbstvertrauen mit kleinen Komplimenten.

So:

mit → dative
plural dative → Komplimenten
adjective ending → kleinen

What does aber do in this sentence, and why is the verb in second position?

Here aber is a coordinating conjunction meaning but.

In German, coordinating conjunctions like und, oder, aber, denn:

do not change the word order of the clause that follows.
the clause after them is a normal main clause with verb in second position.

So:

Die Anfängerin ist noch unsicher, aber die Fortgeschrittene stärkt ihr Selbstvertrauen …

Second clause:

Subject: die Fortgeschrittene
Verb: stärkt (in 2nd position)
Object: ihr Selbstvertrauen
Prepositional phrase: mit kleinen Komplimenten

This is different from subordinating conjunctions like weil, dass, which push the verb to the end of the clause.

What is the difference between ist noch unsicher and fühlt sich noch unsicher?

ist noch unsicher
literally: “is still insecure / unsure”.
It describes a state or characteristic.
fühlt sich noch unsicher
literally: “still feels insecure / unsure”.
It emphasizes the subjective feeling more strongly.

Both are natural. In a context about confidence and experience, ist noch unsicher is perfectly fine and idiomatic.
If you want to stress the internal, emotional experience, you can use fühlt sich noch unsicher.

Is there a difference between Selbstvertrauen and Selbstbewusstsein here?

Both are often translated as self-confidence, but there is a nuance:

Selbstvertrauen
literally “trust in yourself” → confidence that you can do things, belief in your abilities.
Selbstbewusstsein
literally “being aware of yourself” → self-awareness, self-assurance, often also “confidence”, sometimes with a bit more emphasis on presence / bearing.

In this sentence, you could say either:

… stärkt ihr Selbstvertrauen …
… stärkt ihr Selbstbewusstsein …

Both would be understood as “strengthens her self-confidence”.
The original choice Selbstvertrauen fits very naturally with the idea of a beginner who doesn’t yet trust her own abilities.

How would I say this sentence in the plural, e.g. “The beginners are still insecure, but the advanced learners…”?

You would pluralize both Anfängerin and Fortgeschrittene:

Die Anfängerinnen sind noch unsicher, aber die Fortgeschrittenen stärken ihr Selbstvertrauen mit kleinen Komplimenten.

Notes:

Anfängerin → Anfängerinnen (regular feminine plural).
Fortgeschrittene → Fortgeschrittene (plural looks the same as singular feminine, but you see it from the verb and context).
Verb agreement:
- sind for plural beginners.
- stärken for plural advanced learners.
ihr Selbstvertrauen could now mean their self-confidence (plural) in context; you might clarify with:
- deren Selbstvertrauen (their [the beginners’] self-confidence).

Is it natural in German to say that you “strengthen someone’s self-confidence with small compliments”?

Yes, the phrasing is natural and idiomatic:

jemandes Selbstvertrauen stärken – to strengthen / boost someone’s self-confidence
mit kleinen Komplimenten – with small compliments

You could hear very similar real-life sentences, for example in teaching or coaching contexts.
Alternative but still natural variants:

… stärkt ihr Selbstvertrauen durch kleine Komplimente.
(through small compliments)
… gibt ihr mit kleinen Komplimenten mehr Selbstvertrauen.
(gives her more self-confidence with small compliments)

The original wording is fully correct and sounds good.