Dobre wykształcenie pomaga, ale jeszcze ważniejsza jest umiejętność rozmowy z ludźmi.

Because wykształcenie is a neuter singular noun, and the adjective has to agree with it.

• dobry = masculine singular
• dobra = feminine singular
• dobre = neuter singular

So:

• dobre wykształcenie = good education

This is the nominative singular form, because wykształcenie is the subject of the first clause.

Wykształcenie usually means education in the sense of a person’s educational background, level of schooling, or formal education.

So in this sentence, dobre wykształcenie pomaga means something like:

• A good education helps
• Good education is helpful

It is not talking about educating someone as an action. It is talking about the result or possession of education.

Pomaga is the 3rd person singular present tense of pomagać = to help.

The subject is dobre wykształcenie, which is singular, so the verb is singular too:

• dobre wykształcenie pomaga = good education helps

Even though education is an abstract idea, Polish still treats it grammatically as a singular noun, so the verb is singular.

• ale = but
• ważniejsza = more important (feminine singular comparative)
• jeszcze here strengthens the comparison: even more, still more

So ale jeszcze ważniejsza means:

• but even more important
• but still more important

In this sentence, jeszcze does not mean still in the time sense. It is intensifying the comparison.

Because ważniejsza has to agree with umiejętność, which is a feminine singular noun.

Agreement:

• ważniejszy = masculine singular
• ważniejsza = feminine singular
• ważniejsze = neuter singular

Since the sentence says ważniejsza jest umiejętność, the adjective matches umiejętność.

Both are possible, but the given word order sounds natural and slightly more emphatic.

• Jeszcze ważniejsza jest umiejętność... puts focus on more important
• Umiejętność... jest jeszcze ważniejsza puts focus more on the skill

Polish word order is more flexible than English. Because cases show grammatical roles, Polish can move words around for emphasis more easily.

So the sentence as written highlights the contrast:

• Good education helps, but even more important is the ability...

That structure sounds quite natural in Polish.

Because umiejętność often takes the genitive case to say the skill/ability of doing something.

So:

• umiejętność = skill, ability
• rozmowa = conversation
• rozmowy = genitive singular form of rozmowa

Therefore:

• umiejętność rozmowy = literally the skill of conversation
• more naturally: the ability to talk, the ability to converse

This is a common pattern in Polish:

• umiejętność pisania = ability to write
• umiejętność prowadzenia rozmowy = ability to carry on a conversation

Because the preposition z meaning with requires the instrumental case.

The basic form is:

• ludzie = people

But after z, it changes to instrumental plural:

• z ludźmi = with people

So:

• rozmowy z ludźmi = talking/conversation with people

This is an important pattern:

• z przyjacielem = with a friend
• z przyjaciółmi = with friends
• z ludźmi = with people

It is irregular, and that is why learners often notice it.

The noun ludzie is the plural form related to człowiek (person, human being), but in practice ludzie functions as people. Its forms are somewhat irregular:

• nominative plural: ludzie
• genitive plural: ludzi
• instrumental plural: ludźmi

So ludźmi is simply the correct instrumental plural form. It is one of those forms you usually just have to learn by exposure and practice.

Yes, absolutely.

• umiejętność rozmowy z ludźmi
• umiejętność rozmawiania z ludźmi

Both are possible.

The second version, with rozmawiania, is a little more explicitly verbal: the ability of talking with people.

The version in your sentence, umiejętność rozmowy z ludźmi, is slightly more compact and elegant. It can sound a bit more like the skill of conversation with people or the ability to talk to people.

Both are natural, but the original sentence sounds polished and idiomatic.

No. You need the preposition z here.

• rozmowa z ludźmi = conversation with people
• rozmowa ludźmi is incorrect

The preposition z shows the relationship with people, and then ludźmi appears in the instrumental because that is the case required by z.

Yes. Polish often uses a singular noun like this to make a general statement.

So Dobre wykształcenie pomaga can mean:

• A good education helps
• Good education helps
• Having a good education helps

English can phrase that idea in several ways, but in Polish the singular noun works very naturally for a general truth.

The sentence has two clauses joined by ale (but):

1. Dobre wykształcenie pomaga

   • subject: dobre wykształcenie
   • verb: pomaga

2. ale jeszcze ważniejsza jest umiejętność rozmowy z ludźmi

   • linking verb: jest
   • predicate adjective: jeszcze ważniejsza
   • noun it refers to: umiejętność rozmowy z ludźmi

A very literal structure would be:

• Good education helps, but even more important is the ability of talking with people.

A natural English version is:

• A good education helps, but the ability to talk to people is even more important.

So the sentence contrasts two things:

• good education
• people skills / communication ability

and says the second is more important.