Ovaj mesec radim više nego prošlog meseca, ali sledeći mesec će biti lakši.

Ovaj mesec is an example of the accusative of time, which Serbian often uses for expressions like this month, this week, this year, etc.

So:

• ovaj mesec = this month / during this month
• ovog meseca can also exist, but it usually sounds more like of this month or appears in other grammatical contexts

Here, ovaj mesec radim... means I am working more this month.

Also note that mesec is a masculine inanimate noun, so its nominative and accusative look the same:

• nominative: ovaj mesec
• accusative: ovaj mesec

That is why the form does not visibly change.

Prošlog meseca is in the genitive, and here it functions as a time expression meaning last month.

So:

• prošlog meseca = last month

The sentence is really comparing the amount of work now with the amount of work last month:

• Ovaj mesec radim više nego prošlog meseca
• literally: This month I work more than last month

Serbian often uses the genitive without a preposition for expressions of time such as:

• prošlog meseca = last month
• prošle godine = last year
• ovog jutra = this morning

Više means more, and nego means than in comparisons.

So:

• više nego = more than

This is the standard way to compare actions, amounts, or degrees:

• Radim više nego ranije. = I work more than before.
• On zna više nego ja. = He knows more than I do.

In this sentence, the comparison is about how much I work, so više nego is exactly what you would expect.

Yes. Serbian often leaves out repeated words if they are easy to understand from context.

The full idea would be something like:

• Ovaj mesec radim više nego što sam radio prošlog meseca.

That means:

• This month I am working more than I worked last month.

But in natural Serbian, the shorter version is very common:

• Ovaj mesec radim više nego prošlog meseca.

English does something similar:

• I’m working more this month than last month.

You do not need to repeat I worked if the meaning is already clear.

Because Serbian usually does not need subject pronouns unless you want emphasis or contrast.

The verb ending already tells you the subject:

• radim = I work / I am working

So ja radim is possible, but it usually sounds emphasized:

• Ja radim više, a on manje. = I work more, and he less.

In your sentence, plain radim is the normal and natural choice.

Because Serbian, like English, often uses the present tense for something happening during a current period of time.

So:

• Ovaj mesec radim više = This month I’m working more

It does not have to mean this exact second. It means that during the current month, this is your general situation.

This is very natural in Serbian:

• Ove nedelje učim više. = This week I’m studying more.
• Ove godine putujem manje. = This year I’m traveling less.

Će biti is the future tense of biti (to be).

So:

• biće or će biti = will be

In your sentence:

• sledeći mesec će biti lakši = next month will be easier

A few useful points:

• će is a future auxiliary
• biti is the infinitive to be
• with many verbs, Serbian forms the future with ću/ćeš/će... + infinitive

Examples:

• Radiću sutra. = I will work tomorrow.
• On će doći. = He will come.
• Sledeći mesec će biti lakši. = Next month will be easier.

With biti, both će biti and biće are common.

Because lakši agrees with the noun mesec, which is masculine singular.

• mesec = masculine singular
• therefore the adjective must also be masculine singular:
  • lakši = easier

So:

• sledeći mesec će biti lakši = next month will be easier

Compare:

• dan će biti lakši = the day will be easier
• nedelja će biti lakša = the week will be easier
• vreme će biti lakše would not fit here, because vreme is neuter and also the meaning would be different

Sledeći is an adjective meaning next or following.

Here it agrees with mesec:

• sledeći mesec = next month

Grammatically, this is again a masculine singular form. Since mesec is masculine singular, the adjective must match it.

You may also hear:

• naredni mesec
• idući mesec

All can mean next month, though usage can vary a little by region or style.

Because Serbian has no articles like English the and a/an.

So Serbian simply says:

• ovaj mesec = this month
• sledeći mesec = next month

The meaning that English expresses with articles is usually understood from context, word order, or other words like:

• ovaj = this
• taj = that
• jedan = one / a certain one

For English speakers, this is very common to notice at first: Serbian does not need an article in front of nouns.

Yes, Serbian word order is more flexible than English, although some versions sound more natural than others depending on emphasis.

Your sentence is very natural:

• Ovaj mesec radim više nego prošlog meseca, ali sledeći mesec će biti lakši.

But you could also hear things like:

• Više radim ovaj mesec nego prošlog meseca.
• Sledeći mesec biće lakši.
  This is possible, though će biti lakši is usually the more neutral word order.

Word order in Serbian often changes for focus or style, not because the basic meaning changes.

Yes. Mesec can mean both month and moon, just like some older poetic usage in English connects the two ideas historically.

The meaning depends on context:

• ovaj mesec = this month
• pun mesec = full moon

In your sentence, it clearly means month because it appears in time expressions:

• ovaj mesec
• prošlog meseca
• sledeći mesec

Both exist, depending on the standard variety.

• mesec is the usual Serbian Ekavian form
• mjesec is the Ijekavian form used in some varieties of Serbian and in closely related standards

So you may see:

• Ovaj mesec...
• Ovaj mjesec...

Both are correct in their own variety. If you are learning standard Serbian as used in most of Serbia, mesec is the form you will most often meet.