Sada spremam torbu, jer sutra rano idem na posao.

Because Serbian usually drops subject pronouns when they are not needed. The verb endings already show who is doing the action.

• spremam = I am preparing / I prepare
• idem = I go / I am going

So ja is not necessary here. You could say Ja sada spremam torbu..., but that would usually add emphasis, like I’m the one preparing the bag.

Spremam is the 1st person singular present tense form of the imperfective verb spremati.

In this sentence, it means something like:

• I am preparing
• I am packing
• I’m getting ... ready

The imperfective verb is used because the action is seen as ongoing or in progress now.

A related perfective verb is spremiti. Compare:

• Sada spremam torbu. = I’m packing/preparing the bag now.
• Spremiću torbu. = I’ll pack/get the bag ready.

Because it is the direct object of the verb spremam, so it goes into the accusative case.

• nominative: torba
• accusative: torbu

This is very common with feminine nouns ending in -a:

• knjiga → knjigu
• voda → vodu
• torba → torbu

So spremam torbu literally means I am preparing/packing the bag.

Not necessarily my bag. Serbian often leaves out possessives when they are obvious from context.

So spremam torbu can mean:

• I’m packing the bag
• I’m packing my bag
• I’m getting the bag ready

If you want to make my explicit, you could say spremam svoju torbu, but that is not always needed.

It can be either, depending on context.

Spremati is a broad verb. It can mean:

• to prepare
• to get ready
• to put in order
• to pack

In this sentence, because the object is torba and the reason is going to work tomorrow, English will often translate it as I’m packing my bag or I’m getting my bag ready.

A more specifically packing verb is pakovati / pakujem, and many speakers could also say Sada pakujem torbu.

Because Serbian often uses the present tense for a planned or expected future action, especially when there is a clear time word like sutra.

So:

• sutra idem na posao = tomorrow I’m going to work

This works much like English in sentences such as Tomorrow I’m leaving early.

Serbian can also use the future tense, but the present is very natural here because the event is already planned or arranged.

Because ići na posao is the normal Serbian expression for to go to work.

Here, na does not mean only physical onto. With certain nouns, it is just the idiomatic preposition used with activities, institutions, or destinations in a functional sense.

So:

• idem na posao = I’m going to work
• idem na fakultet = I’m going to college / university
• idem na sastanak = I’m going to a meeting

u posao would usually mean something different, more like into the work/business, not the normal everyday expression for commuting to work.

It actually is in the accusative, but for this noun the accusative looks the same as the nominative.

• nominative: posao
• accusative: posao

This happens because posao is a masculine inanimate noun. In Serbian, masculine inanimate nouns usually have:

• nominative = accusative

So na posao is accusative, even though the form does not visibly change.

Rano is an adverb meaning early.

It modifies idem:

• sutra rano idem na posao = tomorrow I’m going to work early

It tells you when or how early the action happens. It does not change form here.

Because jer means because and introduces a subordinate clause. In Serbian, a clause introduced by jer is normally separated by a comma.

So the sentence is structured like this:

• main clause: Sada spremam torbu
• subordinate clause: jer sutra rano idem na posao

That is why the comma appears before jer.

Yes. Serbian word order is more flexible than English word order, because case endings and verb forms carry a lot of grammatical information.

The original sentence is very natural:

• Sada spremam torbu, jer sutra rano idem na posao.

But other orders are possible, depending on emphasis:

• Jer sutra rano idem na posao, sada spremam torbu.
• Sutra rano idem na posao, pa sada spremam torbu.

Even so, not every rearrangement sounds equally natural. The original version is a good neutral way to say it.

They both mean now.

• sada is the full form
• sad is a very common shortened form in everyday speech

So these are both natural:

• Sada spremam torbu.
• Sad spremam torbu.

The meaning is basically the same. Sad is just a bit more conversational.