Learn Hardcore Norwegian: Lederen er ansvarlig for planen. - The leader is responsible for the plan.

Lederen: the subject, definite singular of the common-gender noun leder (leader/manager).
er: present tense of å være (to be).
ansvarlig: a predicative adjective describing the subject.
for planen: a prepositional phrase; for introduces the complement of responsibility, and planen is the definite singular of plan (plan).

Why is it for and not another preposition like av, til, or over?

With ansvarlig, the fixed preposition for what someone is responsible for is for: ansvarlig for noe.

ansvarlig overfor noen means responsible/answerable to someone (accountable).
av would mean by/of and is wrong here.
til and over do not collocate with ansvarlig in this sense.

Is ansvarlig an adjective or a noun here?

Here it’s an adjective. It can also be used as a noun meaning “the person responsible”:

en ansvarlig = a person in charge
den ansvarlige (for planen) = the person responsible (for the plan)

How does ansvarlig inflect (singular/plural, gender)?

Adjectives ending in -lig/-ig are special: they do not take a neuter -t.

Predicative, singular (common or neuter): ansvarlig
Predicative, plural: ansvarlige (e.g., Lederne er ansvarlige)
Attributive, indefinite: en ansvarlig leder, et ansvarlig valg, ansvarlige ledere
Attributive, definite: den ansvarlige lederen, de ansvarlige lederne

Should it be ansvarlig or ansvarlige after er when the subject is definite?

It depends on number, not definiteness. Since Lederen is singular, it’s ansvarlig. For plural: Lederne er ansvarlige. Predicative adjectives don’t take the definite -e just because the noun is definite.

Why do both Lederen and planen have the -en ending?

They’re both definite singular forms:

leder → lederen (the leader/manager)
plan → planen (the plan)
Using definite forms signals that the speaker and listener know which leader and which plan are meant.

Could I say the sentence with indefinites instead?

Yes, but the meaning shifts:

En leder er ansvarlig for planen = A (non-specified) leader is responsible for the (specific) plan.
Lederen er ansvarlig for en plan = The (specific) leader is responsible for a (non-specified) plan.
En leder er ansvarlig for en plan = Very generic: A leader is responsible for a plan.

Can I use sjefen instead of lederen?

You can, but nuance differs:

lederen = the leader/manager (neutral, role/title)
sjefen = the boss (more informal/colloquial, hierarchical flavor) Both are common; pick based on tone and context.

Is there another common way to say this using the noun “responsibility”?

Yes:

Lederen har ansvar for planen.
Lederen har ansvaret for planen. (more specific/definite)
All three—er ansvarlig for, har ansvar for, and har ansvaret for—are natural, with minor nuance.

What’s the difference between ansvarlig for and ansvarlig overfor?

ansvarlig for
- thing/task = responsible for something: ansvarlig for planen
ansvarlig overfor
- person/body = accountable to someone: ansvarlig overfor styret (accountable to the board)

Could the sentence mean “The leader is a responsible person” (as a character trait)?

Not with for planen.

Lederen er ansvarlig (alone) can mean “The leader is responsible (as a person).”
Lederen er ansvarlig for planen means responsible for a specific thing (the plan).

Is there a form like ansvarligt in Norwegian?

No, not in Bokmål. Adjectives ending in -lig/-ig don’t take the neuter -t:

et ansvarlig valg, et viktig tema, et mulig svar (not ansvarligt/viktigt/muligt).

How would I express different tenses?

Past: Lederen var ansvarlig for planen. (was)
Future/intended: Lederen skal være ansvarlig for planen.
Becoming: Lederen blir ansvarlig for planen.

Can I front the prepositional phrase for emphasis?

Yes, but keep Norwegian V2 word order (verb in second position):

For planen er lederen ansvarlig.
Here the fronted phrase For planen is first, the verb er is second, then the subject lederen.

How is the sentence pronounced?

Approximate, Eastern Norwegian:

Lederen: “LEH-deh-ren” (the final -en is a light “en”)
er: “ehr”
ansvarlig: “ahn-SVAR-lee” (the final g is usually very soft or silent; many speakers merge rl into a single “dark l” sound)
planen: “PLAH-nen” (long a in plan)

Does this work as a headline without er?

Yes, headline style often drops the verb:

Lederen ansvarlig for planen (newspaper/heading register)

Is there a Nynorsk equivalent?

Yes:

Leiaren er ansvarleg for planen.
Nynorsk uses leiaren (for lederen) and ansvarleg (for ansvarlig). The preposition for stays the same.

How do I say “in charge of” or “responsible for doing something”?

“in charge of”: ansvarlig for (e.g., ansvarlig for budsjettet)
“responsible for doing X”: ansvarlig for å + infinitive (e.g., ansvarlig for å gjennomføre planen)