Learn Finnish: Nuori poika nukkui lippis päässä ja pää kallellaan. - The young boy slept with a cap on his head and his head tilted.

This is an absolute phrase of state. To describe a physical state or how someone is wearing an item of clothing, Finnish puts the item in the nominative case (lippis) followed by the location in a local case, like the inessive (päässä). You do not need a preposition for 'with' or a verb for 'wearing'.

What exactly is the form of kallellaan?

kallellaan is an adverb of state meaning 'tilted' or 'leaning'. It is built from a root word referring to a slant, put into the adessive case (-lla) and then given a third-person possessive suffix (-an). This suffix points back to the subject (the young boy), literally meaning 'on his tilt'.

Why doesn't päässä have a possessive suffix (like päässään), while kallellaan does?

When a body part is in a local case describing the subject's own body, everyday Finnish often drops the possessive suffix because the owner is already obvious from the context, so päässä is perfectly sufficient. However, kallellaan belongs to a class of fixed spatial adverbs. These specific state adverbs always require a possessive suffix that matches the grammatical person they refer to.

Could I use kanssa ('with') instead, like nukkui lippiksen kanssa?