Learn Hardcore German: Die Einrichtung wirkt neu, aber die Anleitung fehlt noch. - The facility looks new, but the instructions are still missing.

No. Here wirkt (from wirken) means "appears/seems/comes across as." To say "works/functions," use funktionieren (for things) or arbeiten (for people). Another common meaning of wirken is "to take effect" (e.g., Die Medizin wirkt).

Why is neu not inflected (no ending)?

Because it's a predicate adjective after a verb like wirken, sein, aussehen, etc. Predicate adjectives in German do not take endings: Die Einrichtung wirkt neu. But before a noun (attributive), you add endings: die neue Einrichtung.

What gender are Einrichtung and Anleitung, and how can I tell this is singular?

Both Einrichtung and Anleitung are feminine nouns (die Einrichtung, die Anleitung). Here they are singular, which you can tell from the verb forms: wirkt and fehlt are 3rd person singular. Plural would be Die Anleitungen fehlen noch.

Does aber change the word order?

No. Aber is a coordinating conjunction; it keeps verb-second order in the clause that follows. So: ..., aber die Anleitung fehlt noch. Compare: a subordinating conjunction like weil would push the conjugated verb to the end: ..., weil die Anleitung noch fehlt.

Why is noch at the end?

Noch is a temporal particle meaning "still/yet." It typically sits in the middle field after the verb; here it comes last because nothing else follows. You can move it for emphasis: Noch fehlt die Anleitung (fronting noch) vs. the neutral Die Anleitung fehlt noch.

Should it be noch nicht instead of noch?

With fehlen, plain noch already expresses "is not there yet." So Die Anleitung fehlt noch is natural. Noch nicht is used when negating another verb: Die Anleitung ist noch nicht da/geliefert.

Difference between wirkt neu, sieht neu aus, and scheint neu (zu sein)?

wirkt neu: "comes across as new" (overall impression, not only visual).
sieht neu aus: "looks new" (visual appearance).
scheint neu (zu sein): "seems/appears to be new" (more tentative, often more formal).

What exactly does Einrichtung mean here?

Einrichtung is flexible. Common meanings:

interior/furnishings/fit-out of a room or building,
setup/installation,
facility/institution (e.g., eine soziale Einrichtung). It usually does not mean a single "device" (that would be das Gerät), though in technical contexts Einrichtung can mean an apparatus or setup.

What does Anleitung refer to, and are there synonyms?

Anleitung is an instruction manual/guide. Close synonyms:

Bedienungsanleitung, Gebrauchsanweisung (user manual),
Handbuch (handbook),
Leitfaden (guide),
For "guidelines/policy," use Richtlinie, not Anleitung.

Why use die Anleitung and not eine Anleitung?

Definite die implies a specific, expected manual for this item/setup. Eine Anleitung would mean "some manual" in general. Both are possible, but the definite article feels natural when you expect the standard manual that should come with the product.

How does fehlen work grammatically?

The thing that is missing is the subject, and any affected person is in the dative:

Die Anleitung fehlt.
Mir fehlt die Anleitung. (I am lacking the manual.) Plural changes the verb: Uns fehlen die Anleitungen.

Is the comma before aber required?

Yes. When aber connects two independent clauses, German requires a comma: Die Einrichtung wirkt neu, aber die Anleitung fehlt noch.

Can I change the word order for emphasis?

Yes, as long as the verb stays in second position:

Noch fehlt die Anleitung. (emphasizes "still/yet")
Die Anleitung fehlt noch immer. / Die Anleitung fehlt immer noch. (stronger "still"; often longer than expected)

Could I use zwar ... aber or doch instead of aber?

zwar ... aber highlights concession: Die Einrichtung wirkt zwar neu, aber die Anleitung fehlt noch.
doch as a conjunction is a bit more formal/literary than aber: ..., doch die Anleitung fehlt noch. All three are correct; aber is the most neutral.

What are the key forms of wirken I should know?

Present: ich wirke, du wirkst, er/sie/es wirkt, wir wirken, ihr wirkt, sie wirken.
Simple past: wirkte.
Perfect: hat gewirkt.

Is there a difference between neu and neulich?

Yes. neu = "new." neulich = "recently." You cannot say Die Einrichtung wirkt neulich; that would be wrong. Use kürzlich/neulich with a verb of time: Die Einrichtung wurde neulich installiert.

What about wirkt wie neu?

Wirkt wie neu means "seems like new/as good as new," implying it may not actually be new but appears almost new. Wirkt neu leans more toward "appears to be new."

Could Einrichtung also mean an "institution" here?

Only if the context makes that reading plausible (e.g., discussing a social or educational institution). In most everyday physical contexts (a room, lab, shop), Einrichtung will be understood as the interior/setup/fittings.