אם השריר בגב עוד כואב, אני לא רוצה לרוץ היום.

אם means if. It introduces the condition:

• אם השריר בגב עוד כואב = if the muscle in the back still hurts

Hebrew uses אם very much like English if in this kind of sentence.

The comma separates the if-clause from the main clause:

• אם השריר בגב עוד כואב, = conditional part
• אני לא רוצה לרוץ היום. = main statement

This is normal Hebrew punctuation when a sentence begins with אם + a condition.

ה־ is the Hebrew definite article, meaning the.

So:

• שריר = a muscle
• השריר = the muscle

In this sentence, the speaker means a specific muscle, so השריר is natural.

בגב means in the back or in [my/the] back, depending on context.

With body parts, Hebrew often leaves possession implied if it is obvious. So:

• השריר בגב can naturally mean the muscle in my back
• השריר בגב שלי is also possible, but more explicit

Hebrew often sounds more natural than English with this kind of omitted possession, especially when the owner is clear from context.

Here עוד means still.

So:

• עוד כואב = still hurts

Be careful: עוד can also mean more, another, or again in other contexts. Here, because it appears with pain, the meaning is still.

A more formal or unambiguous alternative would be עדיין:

• אם השריר בגב עדיין כואב...

That means almost the same thing.

Because it agrees with השריר, which is a masculine singular noun.

• שריר = masculine singular
• therefore כואב = masculine singular

If the noun were feminine, the form would change:

• היד כואבת = the hand hurts

So in this sentence, כואב matches השריר.

No. In Hebrew, simple present-tense sentences usually do not use a word for is / are.

English says:

• the muscle is painful
• the muscle hurts

Hebrew can simply say:

• השריר כואב

So there is no missing word. That is just normal Hebrew grammar.

Because the meaning is I don’t want to run, not I’m not running.

These are different ideas:

• אני לא רוצה לרוץ = I don’t want to run
• אני לא רץ = I’m not running / I do not run

The sentence is talking about desire / willingness, so Hebrew uses:

• רוצה = want
• לרוץ = to run

לרוץ is the infinitive, meaning to run.

The ל־ at the beginning often marks the infinitive in Hebrew:

• לרוץ = to run
• ללכת = to go / to walk
• לאכול = to eat

So רוצה לרוץ literally means want to run.

Yes. That is very common in Hebrew when talking about pain.

For example:

• אם כואב לי הגב... = if my back hurts...
• אם השריר בגב כואב לי... = if the muscle in my back hurts me / is hurting me

The sentence you were given focuses on the muscle as the thing that hurts. Adding לי makes the experiencer more explicit:

• לי = to me

Both patterns are natural, but כואב לי is especially common in everyday Hebrew.

Hebrew word order is fairly flexible, especially with time words like היום.

So these are all possible, with slightly different emphasis:

• אני לא רוצה לרוץ היום = neutral, very natural
• היום אני לא רוצה לרוץ = emphasizes today
• אני היום לא רוצה לרוץ = also possible

Putting היום at the end is a very normal choice.

It is very natural and usually helpful.

In the present tense, Hebrew verb forms like רוצה do not clearly show person by themselves the way some past/future forms do. So אני makes the subject clear:

• אני לא רוצה לרוץ = I don’t want to run

In casual speech, pronouns can sometimes be dropped when the meaning is obvious, but here אני is the standard and clear form.

Mostly only in pronunciation, not in ordinary spelling.

The word רוצה is written the same for both:

• masculine pronunciation: rotzé
• feminine pronunciation: rotzá

So:

• a man says אני לא רוצה לרוץ היום and pronounces רוצה as rotzé
• a woman says the same written sentence, but pronounces רוצה as rotzá

The word כואב does not change here, because it agrees with השריר, and שריר is masculine no matter who is speaking.