So, the use of the definite article to indicate one's own body parts is one thing; is this universally applicable to anything one possesses? Is this always the default understanding or is it only the case with certain types of objects, like clothes? If so, which ones? If I say "Li vendas la domon" will it be understood as his house or the house?
To quote from PMEG (my translation):
"La is often used instead of a possessive pronoun if the context shows clearly who the owner is. That happens in particular when talking about body parts, clothes or relatives. Then "la" is often preferred."
So, in the case of "Li vendas la domon", that would normally be understood as the house.
Ditto here. A Canadian would be unlikely to say "He raised his hat" or even "He lifted his hat." Both sound like ESL direct translations (awkward and stilted, though not grammatically wrong). The standard expression for this once-common gesture of politeness is (at least in my country), "to tip one's hat."
I know "doff one's cap / hat" as a slightly older expression. In usage, I've seen this one more commonly as, "doff one's cap" as a gesture of servility / subordination of a lesser to a superior individual. Eg. "The coachman doffed his cap as the ladies entered the coach."
A tip of the hat is likely to be directed toward someone who is more equal on the social scale.
Sometimes you will encounter translations that might seem odd in the target language due to it being a direct translation.
But it can be necessary in order to show how to think in the source language.
Where you in english, at least from the dictionary's POV, slant or tilt your hat, you put it at a higher level in esperanto. And in my native language, danish, you cause the hat to levitate. All of the actions make sense in some way.