Posle davanja krvi potrebni su osveženje i unos tečnosti.

Because after posle (after), Serbian normally uses a noun phrase, not an infinitive.

• davanje krvi = giving blood / blood donation
• posle davanja krvi = after giving blood / after a blood donation

So davanja is a verbal noun, formed from the verb idea to give.

Davanja is in the genitive singular.

That is because posle requires the genitive:

• posle čaja = after tea
• posle ručka = after lunch
• posle davanja krvi = after giving blood

The base form is davanje. After posle, it becomes davanja.

In the phrase davanje krvi, the word krvi is in the genitive singular.

This happens because davanje is a noun, and nouns like this often take their complement in the genitive:

• davanje krvi = giving of blood
• unos tečnosti = intake of fluids

So the structure is:

• davanje = giving
• krvi = of blood

Then the whole phrase becomes posle davanja krvi.

Potrebni su means are needed / are necessary.

Here:

• su = are
• potrebni = necessary / needed

The subject is osveženje i unos tečnosti — two things joined by i (and), so Serbian uses a plural verb:

• su = plural are

This is why it is not je.

Good question. On its own, osveženje is neuter singular, but the subject here is not just one noun. It is a coordinated subject:

• osveženje i unos tečnosti

Because there are two items, Serbian uses plural agreement. In this kind of structure, potrebni is a common default plural form.

So the sentence is treating refreshment and fluid intake as two needed things together.

Osveženje literally means refreshment.

In this context, it usually means something like:

• a light snack
• a refreshing drink
• refreshments in general

So even though English often says refreshments in the plural, Serbian can use the singular osveženje for the general idea.

Literally, it means intake of liquid / fluid intake.

• unos = intake
• tečnosti = of liquid / fluids

In natural English, this would often be understood as:

• drinking fluids
• fluid intake
• drinking enough liquids

It sounds a bit formal or medical, which fits this sentence.

Tečnosti is in the genitive singular after unos.

This is similar to davanje krvi:

• unos vode = intake of water
• unos tečnosti = intake of fluids/liquid

The noun unos often takes a genitive complement answering intake of what?

So:

• unos = intake
• tečnosti = of fluid(s)

Yes, it sounds fairly formal or instructional, like something you might read in:

• a clinic
• a blood donation center
• a medical leaflet

A less formal everyday version might be closer to:

• Posle davanja krvi treba da se osvežite i da unesete dovoljno tečnosti.

But the original sentence is completely natural in an official or medical context.

Because Serbian does not always express the idea the same way English does.

English might say:

• After giving blood, you need refreshments and fluids.

But Serbian here uses a structure closer to:

• After giving blood, refreshment and fluid intake are necessary.

So instead of saying what you need, it states what is necessary.

Yes. Serbian word order is fairly flexible.

The original:

• Posle davanja krvi potrebni su osveženje i unos tečnosti.

A different order could be:

• Posle davanja krvi osveženje i unos tečnosti su potrebni.

Both are grammatical. The original version sounds a bit more formal and information-focused, which suits medical instructions.

Yes.

• posle = after
• nakon = after

So you could also say:

• Nakon davanja krvi potrebni su osveženje i unos tečnosti.

Nakon often sounds a bit more formal, but both are correct and common.

Yes, very normal.

• davanje krvi = giving blood / blood donation

You may also see related phrases like:

• dobrovoljno davanje krvi = voluntary blood donation
• akcija davanja krvi = blood donation drive

So this is a standard and natural expression.