Transactions that are not fully processed and settled by the merchant are considered pending and do not show when /transactions is called in the Data API. To see pending transactions, use the pending endpoints (instructions for accounts here and cards here).
When does it stop being pending?
After the merchant fully processes the transactions, usually after a couple of days.
Are there any other status possible (e.g failed or reimbursed)?
Not at the moment.
Where can I see the status of a transaction (as there is no field when I fetch transactions)?
Pending transactions are only returned from the /pending endpoints. Settled transactions will come normally from /transactions.
Can a transaction with the same transaction_id be at the same time in the account (or card) transactions and account (or card) pending transactions endpoints?
Unless it is an edge-case or bank error, this should not happen.