Note: all rules quotes below are from the Munchkin rulebook PDF. The same or very similar text is found in the Adventure Time rulebook PDF.
Can you use the "if you discard this card" effect for items you carry?
If you are talking about one-shot items, absolutely (as long as there is not a restriction on the item that you do not meet).
The rules specifically state under "One-Shot" Treasures on page 3 that they:
may be played from your hand or from the table.
This does not specify that they have to be equipped to use.
If you have a different item that is not a one-shot and provides a discard ability, as long as you meet the other requirements (if any), then I would think that it is fine to use with carried items.
What kind of cards can be carried? example can I carry a class card?
No, you cannot carry class cards.
The rules state that only Items can be carried, where an Item is defined in the Items section on page 3 by:
Most Treasures are Items. Items have a Gold Piece
value. (“No Value” is equivalent to zero Gold Pieces, and
these cards are also Items.)
Thus any card with a listed gold piece value (or "No Value") is an Item and can be carried. Class cards do not have a value, nor do they come from the Treasure deck, and therefore cannot be carried.
Is there limits to what I can carry? example I'm carrying 4 armor cards.
You can carry any number of Items that are not Big, but only one Big Item.
The rules state under Big Items on page 3 that:
You may carry any number of Small items, but only one Big
one. (Any item not marked Big is considered Small.)
Can I sell cards for gold that I'm carrying?
Absolutely. Under the Selling Items for Levels section on page 3 it states:
You may sell Items from your hand as well as those you are carrying.
Are cards you carrying considered to be "in play"?
Yes. Under Card Management on page 1 of the rules:
In Play: These are the cards on the table in front of you, showing your Race and Class (if any) and the Items you are carrying.
Some items don't have body icon, is there limits of how many of that type of item I can equip?
There is no limit to how many untyped Items you may have equipped, but where the item has a type there is a limit (for Adventure Time this is the icon in the top left, which is what I assume you mean by the body icon).
Under the Items section of page 3 of the rules:
Anyone can carry any Item ... but you may equip only one Headgear, one suit of Armor, one pair of Footgear, and two “1 Hand” Items (or one “2 Hands” Item)
Any item that does not have a type can be equipped without limit.
