So i went to make all kinds of wooden and stone crafts to sell in trade depot, some of those include crown, scepters, and rings. I noticed that some dwarves would nab this and claim the item as their own. How does this actually work? Would i be able to sell these items that have been claimed by the dwarves? How much items would they continue to hoard?
Dwarves performing a "Store item in stockpile" job on an eligible craft will occasionally "acquire" the object instead of storing it. Some acquired objects can be worn (rings, amulets, bracelets, earrings, crowns), a few can be carried (scepters), while others (figurines, large gems) will just be stashed in their rooms (if chest/floor space is available) or left wherever.
Owned items may not be traded or dumped. Dwarves may continue to acquire items beyond any practical limit (the wiki suggests 220 rings can be worn, which, at a rate of 1 per season, would take 55 game-years to amass). You can easily prevent item acquirement by not storing acquirable items in stockpiles. Conversely, you can encourage item acquirement by creating two or more large, binless craft stockpiles and arranging for them to "give" to each other. Such an arrangement can be fully automated with minecarts to encourage dwarves to select trinkets on a periodic schedule. Note, however, that dwarves who never perform item hauling jobs (because of labors, burrows, other duties, etc.) will not be able to acquire trinkets.
I guess this is something similar with clothing? How does that work too?
Clothing is a different, older system. Dwarves will drop articles of clothing and perform a "Pickup equipment" job whenever they feel their wardrobe is lacking. They may later perform a "Store owned item" job on clothing they dropped, limited by the amount of cabinet/floor space in their rooms.
Ownership will expire in about a month for items that are neither worn/carried by owners nor *unforbidden* inside their rooms. You can "reclaim" stored owned items in vanilla by forbidding them and waiting a month. In older versions, the value of owned objects provided a passive "happiness" boost; it isn't yet known whether they provide a similar benefit in the current stress system.