my question is can an item be the sell of the previous transaction, and at the same time the buy of another one?
you can, it's just like you wasted one chance of transaction. For example, if you bought on Day 1 and sell on Day 5 and bought on Day 5 and sell on Day 10. Profit is P5 - P1 + P10 - P5. It has the same profit as bought on day 1 and sell on day 10(P10 - P1). So it is like that the problem ask you to make at most 2 transactions and you only did one.