Jeśli zgubię notatnik, nie będę pamiętać numerów i ważnych terminów.

Zgubię is from the verb zgubić (to lose, perfective). In Polish, perfective verbs do not have a true present tense. Their non-past forms are used for the future.

So:

• zgubię = I will lose
• not I am losing

This is also normal after jeśli (if). Polish usually uses a future form here, unlike English, which says If I lose..., not If I will lose....

This is about aspect.

• zgubić is perfective → it forms the future with a single simple form: zgubię
• pamiętać is imperfective → it forms the future with będę + infinitive: będę pamiętać

So:

• zgubię notatnik = I will lose the notebook
• będę pamiętać = I will remember

You cannot normally say będę zgubić, because perfective verbs do not form the future that way.

They describe two different kinds of actions/states:

• zgubić is perfective: a single completed event
  
  • to lose
• pamiętać is imperfective: an ongoing state
  
  • to remember

That fits the meaning of the sentence very well:

• first, one thing may happen: I lose the notebook
• then, as a result, a state follows: I won’t remember the numbers and important dates/deadlines

Because notatnik is a masculine inanimate noun, and in the singular accusative, masculine inanimate nouns usually look the same as the nominative.

So:

• nominative: notatnik
• accusative: notatnik

Since zgubić takes a direct object, notatnik is in the accusative, but the form happens to stay the same.

Because the verb is negated: nie będę pamiętać.

In Polish, when a direct object would normally be in the accusative, it often changes to the genitive after negation.

So compare:

• Będę pamiętać numery i ważne terminy.
  I will remember the numbers and important dates/deadlines.
• Nie będę pamiętać numerów i ważnych terminów.
  I won’t remember the numbers and important dates/deadlines.

That is why you get:

• numerów instead of numery
• terminów instead of terminy

Because adjectives must agree with the nouns they describe in:

• case
• number
• gender

Here, ważnych describes terminów, which is genitive plural. So the adjective also has to be genitive plural:

• nominative plural: ważne terminy
• genitive plural: ważnych terminów

That is why you see ważnych, not ważne.

Yes. Both jeśli and jeżeli mean if.

For this sentence, both are correct:

• Jeśli zgubię notatnik, ...
• Jeżeli zgubię notatnik, ...

Very generally:

• jeśli is common and natural in everyday speech
• jeżeli can sound a little more formal or careful

But the difference is small.

Yes. In Polish, a subordinate clause introduced by words like jeśli is normally separated by a comma.

So this is correct:

• Jeśli zgubię notatnik, nie będę pamiętać numerów i ważnych terminów.

If you reverse the order, the comma is still needed:

• Nie będę pamiętać numerów i ważnych terminów, jeśli zgubię notatnik.

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

You can say:

• Jeśli zgubię notatnik, nie będę pamiętać numerów i ważnych terminów.
• Nie będę pamiętać numerów i ważnych terminów, jeśli zgubię notatnik.

Both are correct. The first version is a very natural way to present the condition first. The second puts slightly more focus on the result.

No. Polish also allows a future made with będę plus a past-like form:

• nie będę pamiętać
• nie będę pamiętał (male speaker)
• nie będę pamiętała (female speaker)

These all mean the same thing here.

The version with the infinitive, będę pamiętać, is useful because it does not show gender. That is one reason learners often meet it early.

Because this sentence describes a real possible future condition, not an unreal or hypothetical one.

So Polish uses:

• Jeśli zgubię notatnik... = If I lose the notebook...

If you wanted a more hypothetical idea like If I lost the notebook, I wouldn’t remember..., Polish would use a different structure, typically with gdybym and conditional forms.

So the sentence as given is the normal choice for a realistic future possibility.