Danas nemam novca i ne idem na pijacu.

Because after a negated verb like nemam (I don’t have), Serbian very often uses the genitive instead of the accusative for the thing that is absent.

• novac = nominative singular, money
• novca = genitive singular, of money / any money

So:

• Imam novac. = I have money.
• Nemam novca. = I don’t have any money.

This genitive after negation is very common and is something English speakers usually need time to get used to.

This is a very common question.

In Serbian, ne is usually written separately from the verb:

• ne idem = I am not going
• ne radim = I am not working
• ne znam = I don’t know

But some verbs have special fused negative forms, and imati (to have) is one of them:

• imam = I have
• nemam = I don’t have

So here you get:

• nemam
• but ne idem

That difference is normal and must mostly be learned word by word.

Nemam is the 1st person singular present tense of nemati / negative of imati.

It means:

• I do not have
• I don’t have

Breakdown:

• imam = I have
• nemam = I do not have

The ending -am tells you it is I.

Idem is the 1st person singular present tense of ići (to go).

So:

• idem = I go / I am going

With ne:

• ne idem = I do not go / I am not going

In this sentence, because of danas (today), it is naturally understood as something like I’m not going today.

Serbian often uses the present tense where English uses either:

• simple present: I don’t go
• or present continuous / near-future meaning: I’m not going

So Danas ne idem na pijacu can naturally mean:

• Today I’m not going to the market

The time word danas makes the intended meaning clear. Serbian does not need a separate continuous form like English does.

Danas means today.

It sets the time frame for the whole sentence:

• Danas nemam novca i ne idem na pijacu.

Yes, it can move, because Serbian word order is more flexible than English word order. For example:

• Nemam danas novca i ne idem na pijacu.
• Ne idem danas na pijacu.

But Danas at the beginning is the most straightforward and natural way to emphasize today.

With pijaca (market, especially an open-air market), Serbian normally uses na.

• ići na pijacu = to go to the market
• biti na pijaci = to be at the market

This is just the usual preposition pattern for this noun. English speakers often want to use something like u because they think of into, but Serbian idiom is:

• na pijacu with motion
• na pijaci for location

So you should learn ići na pijacu as a set phrase.

Because after na expressing motion, pijaca goes into the accusative singular.

The noun is:

• nominative: pijaca
• accusative: pijacu

So:

• Pijaca je velika. = The market is big.
• Idem na pijacu. = I’m going to the market.

This -a → -u change is very common for feminine nouns in the singular accusative.

Usually pijaca means an open-air market or farmers’ market, where people buy things like:

• fruit
• vegetables
• cheese
• eggs
• flowers

It is not usually the same as a supermarket. So na pijacu often sounds more like:

• to the market
• to the farmers’ market

depending on context.

In Serbian, each verb is normally negated separately.

So:

• nemam = I don’t have
• ne idem = I’m not going

If you have two actions and both are negative, both verbs must show negation:

• Danas nemam novca i ne idem na pijacu.

English works similarly here:

• I don’t have money and I’m not going to the market.

So the second ne is necessary.

Yes, that is a very natural interpretation, even though Serbian only literally says:

• Today I don’t have money and I’m not going to the market.

The idea is probably that the lack of money is the reason for not going. Serbian leaves that connection implied here.

If you wanted to make the cause more explicit, Serbian could say something like:

• Danas nemam novca, pa ne idem na pijacu.
• Danas nemam novca, zato ne idem na pijacu.

But the original sentence is perfectly natural.

Yes. In negative sentences, the genitive often gives the sense of:

• no money
• any money
• not any money

So nemam novca often feels very close to:

• I don’t have any money
• I have no money

That is one reason the genitive is used so often after negation.

Yes, you could. Serbian word order is flexible, and different orders shift emphasis.

Compare:

• Danas nemam novca i ne idem na pijacu.
  Neutral: Today is the main frame.

• Ne idem na pijacu danas.
  Stronger focus on today as the specific time.

• Na pijacu danas ne idem.
  More marked; stronger emphasis or contrast.

So the original order is neutral and very good for learners, but other orders are possible.