A new ticket goes to the department you chose, with your priority and - if you set one - the related service. That is why setting it matters: whoever answers is already looking at the right product.
Replies arrive two ways at once: on the ticket's page and by email to your account address. Answering the email or replying on the page are the same conversation.
All your tickets are under Help → My Tickets. A ticket stays open while the conversation is live. Once resolved it is closed - but replying to a closed ticket opens it again.
Attachments can be added to any reply, not just the first message.