What happen if my connection is lost or my browser crashes during mid of transfer? Where should I contact in case I need help for my transaction
If I understand it correctly as soon as you send your transaction you no longer need to stay on the page.
Yeah, that's right

Just start a mixing process, download the Letter of Guarantee or save your order number, send your Bitcoin amount to the input address and then you can close the page.
You can always return to the payment page by visiting the "Order Status" link.
Even if you never visit the payment page again, your transaction will be executed automatically.