Ta tłumaczka dobrze mówi po polsku i po angielsku.

Because tłumaczka is a feminine singular noun, and ta is the matching feminine singular form of ten/ta/to.

So:

• ten tłumacz = a male translator/interpreter
• ta tłumaczka = a female translator/interpreter

Polish words like ten/ta/to have to agree with the noun in gender, number, and case.

Also, ta literally means this. Polish has no articles like the or a, so sometimes ta can feel a bit article-like in English, but it is still a demonstrative word, not an article.

You can often leave it out if the context is clear:

• Tłumaczka dobrze mówi po polsku i po angielsku.

Tłumaczka is the feminine form of tłumacz. It can mean either:

• translator
• interpreter

Polish often uses the same basic word for both, and the exact meaning depends on context.

So in this sentence, tłumaczka could mean a woman who translates written text, interprets speech, or simply someone whose profession involves translation.

Because dobrze is an adverb, and it modifies the verb mówi.

• dobry / dobra / dobre = adjective = good
• dobrze = adverb = well

In this sentence, the idea is speaks well, not is good.

So:

• dobra tłumaczka = a good translator
• dobrze mówi = speaks well

This is very similar to the English difference between good and well.

Because this is the normal Polish pattern for saying that someone speaks a language:

• mówić po polsku = to speak Polish
• mówić po angielsku = to speak English
• mówić po niemiecku = to speak German

So after mówić, Polish usually uses po + language form.

For an English speaker, it may feel like Polish is saying speaks in Polish rather than directly speaks Polish. That is a good way to remember it.

A different verb is znać, which means to know:

• Zna polski i angielski = She knows Polish and English

That focuses more on knowledge of the languages, while mówi po polsku focuses on speaking.

Because after po in this expression, Polish uses a special fixed form:

• po polsku
• po angielsku
• po francusku
• po hiszpańsku

So you should learn these as set expressions meaning in Polish, in English, and so on.

For a learner, the safest approach is:

• do not try to build this from the basic dictionary form
• memorize po polsku, po angielsku, etc. as whole phrases

So po polski and po angielski are not correct here.

Yes, in normal standard Polish, it is best to repeat it:

• po polsku i po angielsku

That is the most natural and safest version.

Even though English would usually not repeat in in a similar structure, Polish normally does repeat po here. So learners should copy the pattern exactly.

Yes. Polish word order is more flexible than English word order.

Your sentence is perfectly natural:

• Ta tłumaczka dobrze mówi po polsku i po angielsku.

But you can also say:

• Ta tłumaczka mówi dobrze po polsku i po angielsku.

Both are correct. The difference is mostly about emphasis and rhythm, not basic meaning.

Putting dobrze before mówi slightly highlights how well she speaks. Putting it after the verb sounds natural too.

You can often leave ta out.

• Ta tłumaczka dobrze mówi po polsku i po angielsku. = This translator speaks Polish and English well.
• Tłumaczka dobrze mówi po polsku i po angielsku. = The translator / a translator speaks Polish and English well, depending on context.

Use ta when you want to point to or identify a specific translator, especially if there are several people and you mean this one.

Yes, but it is not exactly the same.

• mówi po polsku i po angielsku focuses on the ability to speak
• zna polski i angielski focuses on knowing the languages

In many situations they are close in meaning, but not identical.

For example, someone might znać a language quite well but not mówić it very fluently. So in your sentence, mówi is the better choice if the point is speaking ability.