Learn Italian: Ha sonno; lo sto coccolando nel passeggino. - He is sleepy; I am cuddling him in the stroller.

Yes! When using the progressive form (stare + gerund), you have two options for pronoun placement. You can either place it before the conjugated verb (lo sto coccolando) or attach it directly to the end of the gerund (sto coccolandolo). Both are completely correct and common.

Why does the sentence use ha (he has) instead of an equivalent for "he is" to mean sleepy?

Italian uses the verb avere (to have) for many physical sensations where English uses "to be". Sonno is a noun meaning "sleep", so ha sonno literally translates to "he has sleep". You do this with other feelings too, like avere fame (to be hungry) and avere freddo (to be cold).

What is the infinitive form of coccolando?

The infinitive is coccolare, which means "to cuddle" or "to pamper". Because it is an -are verb, its gerund (the "-ing" form) is made by replacing the ending with -ando.

Why does the sentence use nel instead of just in?

Nel is an articulated preposition, which means it combines the preposition in with the definite article il (the). Since passeggino is a masculine singular noun, you need the article to say "in the stroller", which forces in + il to merge into nel.