We were also on this cruise and loved loved loved it! Some comments:
We stayed one night in Copenhagen before the cruise at the Adina Apartment Hotel, which I'd highly recommend. We had a very nice, clean 2br apartment with laundry facilities. There's a great pastry shop right around the corner and the Little Mermaid was a short walk away and it was also close to the ship. There were many families heading do the Magic from there on the morning of the 30th.
We booked a private tour in St Petersburg through TJ and it was SO great. We covered a lot of ground starting right at 9am (no trouble for us getting through customs and I'm surprised to hear others did have trouble!). Met the guide and took off for a couple of photo stops, went into a church (not on our original itinerary, so I'm not sure which one) and then drove to Peterhof. Hydrofoil back to the city. Quick tour of the highlights at the Hermitage, lunch, Peter and Paul Fortress, chocolate store, matryoshka doll painting class, photo stop at church of spilled blood, souvenir shopping, back to ship around 7:45pm.
Other than that tour, we did our own thing in all the other cities. We used the walking tour in the Rick Steve's guide for Tallinn and enjoyed it- that and lunch took up the whole time in port. I agree with the person that was a bit disappointed in Helsinki. We also didn't love that city, though our lunch was great (the Lapland stall in the open air market). We thought about doing a sauna, but ultimately decided against it because we thought our kids would get bored. Stockholm was probably our favorite city of the trip. It was the cleanest, prettiest city I think I've ever seen. We did the Rick Steves walking tour of the old town, had a drink at the Ice Bar, saw the changing of the guard, had a wonderful al fresco lunch, went to Junibaken to see the Pippi Longstocking exhibit, and then spent about 1.5 hours at Skansen before heading back to the ship. We could have spent at least another day or 2 there- there was so much to do!
We used credit cards almost exclusively the entire time. I think the first time we took out cash was in Helsinki in order to buy lunch. Oh, we did need cash for lunch in St Petersburg, but our guide changed some money for us on the fly.
We didn't find the boarding process chaotic or confusing at all. Our port arrival time was 12:00-12:30, there was no line to check in when we arrived and there was a separate line for first timers vs everyone else. We did have one hiccup because my son was actively throwing up at the time so we had to check that off on the Ebola form. A quick phone call with the medical staff on board and we were cleared to board though. We got boarding group 12 which was called pretty much immediately after we were done checking in at the counter. The whole process moved along very quickly.
After the cruise, we spent 1 night in Copenhagen and spent half the day exploring the city and the other half at Tivoli, which my kids loved!