Wieczorem znajduję w słowniku nowe słowa i zapisuję je w zeszycie.

In Polish, the subject pronoun is often omitted because the verb ending already tells you who is doing the action. Both znajduję and zapisuję end in -ę, which shows 1st person singular, so the meaning is clearly I find and I write down.

You could add ja if you wanted emphasis, contrast, or clarification, but in a neutral sentence it is usually left out.

Wieczorem means in the evening. It is not the basic dictionary form of the noun.

• wieczór = evening
• wieczorem = in the evening

This is a very common Polish time expression. Polish often uses special adverbial forms like this for parts of the day or times:

• rano = in the morning
• wieczorem = in the evening
• nocą = at night
• latem = in summer

So wieczorem is the natural form here, not wieczór.

Yes. The exact meaning depends on context.

• In a sentence about habits or routines, wieczorem usually means in the evening
• In a one-time situation, it can mean this evening

In your sentence, because the verbs are in the present tense and describe a repeated action, the most natural meaning is in the evening.

Polish uses the present tense for habitual or repeated actions, just like English does in sentences such as I read in the evening or I write new words in a notebook.

So here the present tense does not have to mean only right now. It can also describe a routine:

• Wieczorem znajduję... i zapisuję... = In the evening I find... and write them down...

Both verbs are also imperfective, which fits repeated or ongoing actions very well.

Because znajdę and zapiszę are perfective forms, and in Polish perfective verbs do not have a true present tense. Their so-called present forms usually refer to the future.

So:

• znajduję, zapisuję = imperfective, used for habits or ongoing actions
• znajdę, zapiszę = perfective, usually future, meaning something like I will find, I will write down

Since the sentence describes a regular activity, the imperfective forms znajduję and zapisuję are the right choice.

Literally, znajduję means I find. In this sentence it suggests that you find or come across new words in the dictionary.

That is understandable, but it is not always the most natural Polish way to say I look up words. If you specifically want the idea of checking a word in a dictionary, Polish often uses verbs like:

• sprawdzam słowa w słowniku = I check words in the dictionary
• wyszukuję słowa w słowniku = I search for words in the dictionary

So znajduję is fine literally, but it is slightly different in nuance from English look up.

Here zapisuję is closer to I write down, I note down, or I record than to plain I write.

That is because zapisywać / zapisać often has the sense of putting something down so you keep it, remember it, or have a record of it.

So in this sentence:

• zapisuję je w zeszycie = I write them down in a notebook

If you simply wanted the general idea of writing, piszę would be more basic.

Because w here means in, and it describes location, so Polish uses the locative case.

The noun słownik changes like this:

• słownik = dictionary
• w słowniku = in the dictionary

This is very common after w when it means location:

• w domu = in the house
• w sklepie = in the shop
• w słowniku = in the dictionary

So the ending -u shows that słownik is in the locative singular.

Because nowe słowa is the direct object of znajduję, so it is in the accusative plural.

The singular noun is:

• słowo = word

Its plural is:

• słowa = words

Since słowo is a neuter noun, its accusative plural is the same as its nominative plural. That is why you get:

• nowe słowa = new words

The adjective nowe agrees with słowa in number, gender, and case.

A form like nowych słów would be genitive plural, not the form needed here.

Je means them. It refers back to nowe słowa.

Polish uses different pronoun forms depending on case and sometimes also on whether the noun is masculine personal. Here słowa is not masculine personal, so the normal direct-object form is:

• je = them

So:

• zapisuję je = I write them down

Using ich here would not be the standard choice for this sentence.

W zeszycie means in the notebook and focuses on the place where the words are written.

• zeszyt = notebook / exercise book
• w zeszycie = in the notebook

With zapisywać, this is very natural, because you are talking about writing something in the notebook.

Do zeszytu can appear with some verbs when the idea is more like movement or putting something into the notebook as a target, but with zapisuję the phrase w zeszycie is completely normal and idiomatic.

No, Polish word order is quite flexible. The sentence as given is a neutral, natural order:

Wieczorem znajduję w słowniku nowe słowa i zapisuję je w zeszycie.

This order works well because:

• Wieczorem sets the time first
• then the first action is given
• then the second action follows

You can move parts around, but the emphasis changes. For example, if you put nowe słowa earlier, you give them more focus. If you move wieczorem, the sentence may sound less neutral or more marked.

So the word order is not fixed, but the version you have is a very natural one.