Razmišljam o davanju krvi.

Because the preposition o normally requires the locative case when it means about / concerning.

• base form: davanje
• locative singular: davanju

So:

• Razmišljam o davanju krvi. = I’m thinking about donating blood.

This is a very common pattern in Serbian:

• pričam o poslu = I’m talking about work
• mislim o tome = I’m thinking about that
• razmišljam o putovanju = I’m thinking about traveling / a trip

So the key point is: o + locative.

Davanje is a verbal noun. It comes from the verb davati (to give, imperfective) and turns the action into a noun:

• davati = to give
• davanje = giving

In this sentence, davanje krvi literally means the giving of blood, which in natural English is donating blood or blood donation.

Serbian often uses this kind of noun where English might prefer an -ing form:

• čitanje = reading
• pisanje = writing
• učenje = studying / learning
• davanje krvi = donating blood

Because krvi is the genitive form of krv.

The noun davanje often takes what would be the object of the verb in the genitive:

• davanje čega? = giving of what?
• davanje krvi = giving of blood

So even though krv is the dictionary form, after the verbal noun davanje you get:

• krv → krvi

This is very similar to other Serbian noun phrases built from verbal nouns:

• čitanje knjige = reading a book / the reading of a book
• pisanje pisma = writing a letter / the writing of a letter
• davanje krvi = donating blood / the giving of blood

Because Serbian verbal nouns are usually formed from the imperfective verb.

Here the pair is:

• davati = imperfective
• dati = perfective

So the normal verbal noun is:

• davanje from davati

That does not mean the action must be repeated many times. It is simply the standard way Serbian builds this noun.

So davanje krvi is the natural expression, even if you mean one future blood donation.

Usually it sounds like the idea or act of donating blood in general, not necessarily one completed event.

Razmišljam o davanju krvi suggests:

• I’m considering donating blood
• I’m thinking about blood donation

It focuses on the activity/concept rather than on a single finished act.

If you want to sound more specifically like I’m thinking about giving blood once / I’m thinking that I might give blood, Serbian often uses a clause instead:

• Razmišljam da dam krv.
• Razmišljam o tome da dam krv.

Those feel a bit closer to I’m thinking of giving blood in the sense of a possible concrete action.

Yes. That is also natural, but the structure is a little different.

Compare:

• Razmišljam o davanju krvi.
  = I’m thinking about donating blood.
  This sounds a bit more abstract or topic-like.

• Razmišljam da dam krv.
  = I’m thinking of giving blood.
  This sounds a bit more like I may actually do it.

• Razmišljam o tome da dam krv.
  = I’m thinking about giving blood.
  This combines both ideas and is very natural too.

So all of these can work, but the original sentence uses a noun phrase after o.

Because Serbian has no articles.

English says:

• the blood
• a donation
• the giving of blood

Serbian does not use separate words like a/an/the. The meaning is understood from context.

So:

• davanje krvi can mean giving blood, the giving of blood, or sometimes blood donation, depending on context.

This is normal in Serbian and not something missing from the sentence.

Yes, very common.

In everyday Serbian, davanje krvi is a normal and idiomatic way to talk about blood donation. You will also hear:

• dobrovoljno davanje krvi = voluntary blood donation
• akcija davanja krvi = a blood donation drive / campaign

Another possible expression is:

• doniranje krvi

But davanje krvi is very standard and very widely used.

Yes, Serbian word order is fairly flexible, but the neutral order here is:

• Razmišljam o davanju krvi.

You could sometimes move words around for emphasis, but in this short sentence the standard version is best.

For example, changing the order to something unusual might sound marked or poetic rather than normal conversation. So for a learner, the safest choice is to keep:

• Razmišljam o davanju krvi.

A natural pronunciation is roughly:

• Razmišljam = raz-MISH-lyam
• o = short o
• davanju = da-VA-nyu
• krvi = KR-vee

A few useful pronunciation notes:

• lj in razmišljam is a single Serbian sound, similar to the lli in some pronunciations of million.
• nj in davanju is also a single sound, similar to the ny in canyon.
• krvi can feel tricky because of the consonant cluster krv-. Serbian allows clusters like this much more freely than English does.

There are two different case relationships here:

• o davanju → locative, because of the preposition o
• krvi → genitive, because it depends on the noun davanje

So the structure is:

• razmišljam
• o + locative → o davanju
• davanje + genitive → krvi

That is why you get both davanju and krvi in the same phrase.