המורה אמרה שהיום נלמד דקדוק חדש, אבל קודם נחזור על כלל אחד חשוב.

Because המורה means the teacher, and in Modern Hebrew מורה can refer to either a male or a female teacher. The noun form here does not change, so the verb shows the teacher’s gender.

• אמרה = she said
• אמר = he said

So this sentence is referring to a female teacher.

It means that. Hebrew very often uses ש־ as a short attached conjunction.

So:

• שהיום = that today

A more formal word for that is כי, but ש־ is extremely common in everyday Hebrew.

נלמד is the 1st person plural future form of ללמוד.

So it means:

• we will learn

Hebrew verbs often include the subject inside the verb itself, so you do not need a separate word for we.

Because Hebrew verbs already show person and number.

• נלמד = we will learn
• נחזור = we will review / go back

You can add אנחנו for emphasis, but it is usually unnecessary.

Because Hebrew adjectives usually come after the noun they describe.

So:

• דקדוק חדש = literally grammar new

Also, the adjective must agree with the noun in gender, number, and definiteness. Here דקדוק is masculine singular, so the adjective is חדש, also masculine singular.

Hebrew has a definite article, ה־, meaning the, but it does not have an indefinite article like a/an.

So דקדוק חדש just means new grammar. English sometimes needs a/an, but Hebrew does not.

Here קודם means first or before that.

It shows sequence:

• first we will review
• then we will learn the new grammar

So אבל קודם is something like but first.

Because לחזור על is a common Hebrew expression meaning to go over, to repeat, or to review.

Compare:

• לחזור = to return / go back
• לחזור על something = to repeat / review that thing

So נחזור על כלל means we will review a rule.

With the number one, Hebrew usually places אחד / אחת after the noun.

So:

• כלל אחד = one rule

Then the adjective comes after that whole phrase:

• כלל אחד חשוב = one important rule

That word order is normal in Hebrew.

Because את is used before a definite direct object, and דקדוק חדש is indefinite.

Compare:

• נלמד דקדוק חדש = we will learn new grammar
• נלמד את הדקדוק החדש = we will learn the new grammar

So in this sentence, את is not needed.

Here it clearly means today.

The same spelling can appear in different contexts, but in this sentence:

• שהיום נלמד... = that today we will learn...

So context tells you the meaning.

Yes. In Hebrew, short prefixes are usually attached directly to the following word in writing.

So:

• ש־
  • היום = שהיום

The same thing happens with other common prefixes such as:

• ו־ = and
• ב־ = in
• ל־ = to
• כ־ = as / like

So this spelling is completely normal.