Questions & Answers about Želim da udomim mačku.
Here, da introduces a subordinate verb clause. In sentences like this, it often does the job that English to does in to adopt.
So Serbian says:
Želim da udomim...
where English says:
I want to adopt...
It is not best understood as a literal word-for-word that here.
Because that is a very common Serbian pattern after verbs of wanting, planning, trying, and similar ideas.
So Želim da udomim mačku is the normal, natural Serbian structure.
The infinitive udomiti exists, but in modern Serbian, da + present tense is usually more natural in this kind of sentence.
Because the subject of that second verb is still I.
In Serbian, after da, the verb is normally fully conjugated:
- Želim da udomim mačku = I want to adopt a cat