Frihamnen to Airport

We are planning on booking a Costa Mediterranean cruise out of Stockholm next June. We expect the ship to embark/disembark from Frihamnen. The ship will arrive at Stockholm on Friday, June 16 and we will officially disembark on Saturday, June 17. However, I am interested in taking a very early morning flight back to the San Francisco Bay Area. Actually, there are two flights I am looking at, one leaves at 9:40am and the other at 10:35am. If we book the former flight, I expect we must leave the ship before 7:00am We intend to catch a taxi to airport. The questions are: Will there be taxis available at that early hour at the cruise terminal? Is there any immigration/customs process before leaving the cruise terminal?

Not sure about the taxis, but there won't be any customs or immigration at the pier.

If you want to take a taxi, I think you will need to book one in advance.