If I made a SEPA purchase and the transaction is waiting for the payment confirmation, can I close bitsquare or bitsquare must remain running until the transaction is completed?
It’s safe to close it.
Edit: I’d like to elaborate a bit more:
The Bitsquare client needs to run in order to show your offers in the offerbook. When you close the client during a trade, you at least want to check it often to be able to take action in a timely manner. This is in the interest of both parties. If it takes you too long (time window depends on the payment method) to react during the trade or eventual dispute, you might be violating the protocol and are at risk of losing funds.
Applying common sense is always a good idea: No one likes to wait longer than necessary, but it’s fine to close the client during a trade.