Can I exchange the sentence " How do they come packaged" with "How do they packaged"? What is the function of the word "come"?
"How do they come packaged?"
Because of the word packaged, the verb come in this context aligns with Definition #5 in NOAD:
come (v.) be sold, available, or found in a specified form : the cars come with a variety of extras | they come in three
Your suggested alternate wording is close:
How are they packaged?
means essentially the same thing (you need to use are, instead of do).
Had you not used the word packaged, though, the situation would change slightly:
"How do they come?"
could be changed to:
"How will they arrive?"
This aligns with Definition #1 in NOAD:
come (v.) arrive at a specified place : my trunk hasn't come yet
Most often the usage they come packaged complete with batteries and manual is used to indicate additional items that are included while they are packed in sets of three is used to indicate groupings and they will arrive packed in plain brown paper indicates the style of packaging. Note that the last of these implies that the content would cause embarrassment if identifiable from the packaging.