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.
as far as I know there is no hard rule giving the definite article the possessive meaning. So it might be that by convention it is often used this way, but if you need to be clear (for example in a multiple hat context ;-) ), you should opt for "sian ĉapelon".
Raising his hat implies that the hat came off of his head, tipping on the other hand typically is used to refer to motion that does not require removing the hat.
While the meaning of these gestures is similar, the gestures themselves are different
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.
Exactly. People get so focused on whether the English sentence sounds natural. That would make sense if our goal here was writing perfect English texts - but that's not the goal here.
My wife and daughter agree. On the fifth or sixth playing, one thought maybe it was "levis" but they agree pretty strongly that it sounds like "legis"
Can you say: 'Li levigis la cxapelon'?