Ta kandydatka ma dobre wykształcenie i umiejętność spokojnej rozmowy z ludźmi.

Because kandydatka is a feminine singular noun, and ta is the feminine singular form of this.

Polish demonstratives must agree with the noun in:

• gender
• number
• case

So:

• ten = masculine
• ta = feminine
• to = neuter

Since kandydatka is feminine, ta kandydatka is correct.

Kandydatka means a female candidate, while kandydat means a male candidate or sometimes a candidate of unspecified sex in more general contexts.

The ending -ka is a common way to form feminine nouns in Polish:

• kandydat → kandydatka
• student → studentka
• nauczyciel → nauczycielka

So this sentence specifically refers to a woman.

It is in the nominative singular, because it is the subject of the sentence.

You can identify it by asking: Who has good education and the ability...? Answer: ta kandydatka.

So:

• ta kandydatka = subject = nominative
• ma = verb
• the things she has are the objects

Because wykształcenie is a neuter noun, so the adjective must agree with it.

The adjective dobry changes by gender:

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

So:

• dobre wykształcenie = correct

Also, after ma, this noun phrase is in the accusative, but for many neuter singular nouns, the nominative and accusative look the same. So you still see dobre wykształcenie.

They are in the accusative, because mieć normally takes a direct object in the accusative.

So in this sentence, the candidate has:

• dobre wykształcenie
• umiejętność spokojnej rozmowy z ludźmi

However, the forms do not obviously change here:

• wykształcenie is neuter singular, and its nominative and accusative are the same
• umiejętność is a feminine noun ending in -ść, and its nominative and accusative are also the same

So the case is accusative, even though the form looks unchanged.

It is a noun, not an adjective. It means education, especially in the sense of educational background or level of education.

So:

• dobre wykształcenie = good education / a good educational background

It is usually treated as an uncountable or abstract noun in this kind of sentence. Polish often uses mieć wykształcenie in the same way English says have an education or have a good education.

Because umiejętność often takes a genitive noun to express the ability/skill of something.

So:

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

Literally, the structure is something like:

• ability of calm conversation with people

This is a very normal Polish pattern with abstract nouns.

Compare:

• umiejętność pisania = ability to write / writing skill
• umiejętność pracy w zespole = ability to work in a team
• umiejętność spokojnej rozmowy z ludźmi = ability to have a calm conversation with people

Because spokojnej must agree with rozmowy, and rozmowy is in the genitive singular.

The base noun is:

• rozmowa = conversation

In this phrase it becomes:

• rozmowy = of conversation

So the adjective also changes:

• spokojna rozmowa = a calm conversation
• spokojnej rozmowy = of a calm conversation

This is normal adjective agreement:

• same gender: feminine
• same number: singular
• same case: genitive

Because the preposition z meaning with requires the instrumental case.

The basic plural form is:

• ludzie = people

But after z, it becomes instrumental plural:

• z ludźmi = with people

This is an important pattern:

• z kobietą = with a woman
• z mężczyzną = with a man
• z ludźmi = with people

The form ludźmi is irregular-looking, so it is worth memorizing.

Yes. In Polish, mieć is very often used with abstract nouns to describe what someone possesses as a quality, trait, or qualification.

For example:

• ma doświadczenie = has experience
• ma talent = has talent
• ma cierpliwość = has patience
• ma dobre wykształcenie = has a good education
• ma umiejętność spokojnej rozmowy z ludźmi = has the ability to talk calmly with people

This is completely natural Polish.

Yes. Polish often allows both a noun-based and a verb/adjective-based version.

For example, you could say:

• Ta kandydatka jest dobrze wykształcona i umie spokojnie rozmawiać z ludźmi.
• Ta kandydatka ma dobre wykształcenie i potrafi spokojnie rozmawiać z ludźmi.

The original sentence is a bit more formal and CV/interview-like, because it uses nouns such as wykształcenie and umiejętność.

No, Polish word order is fairly flexible. The given order is natural and neutral:

• Ta kandydatka ma dobre wykształcenie i umiejętność spokojnej rozmowy z ludźmi.

But other orders are possible if you want different emphasis. For example:

• Ta kandydatka ma umiejętność spokojnej rozmowy z ludźmi i dobre wykształcenie.
• Dobre wykształcenie ma ta kandydatka...
  This sounds more marked or contrastive.

So the original version is probably the most straightforward, neutral choice.

Because Polish has no articles.

English needs words like:

• a
• an
• the

Polish usually does not use anything equivalent. Meaning is understood from context.

So:

• kandydatka can mean a candidate or the candidate, depending on context
• ta kandydatka specifically means this candidate

So ta is not an article. It is a demonstrative word meaning this.