1) The cable car doesn't run from Barceloneta, but from Montjuic to Port Vell. Unfortunately, it is closed from Oct 3rd until first quarter of 2006 for renewal works (see the note at
http://www.tmb.net/en_US/barcelona/moute/planols/planoteleferic.jsp .) All information you need about public transport in Barcelona at
http://www.tmb.net/en_US/home.jsp (English version)
2) There is a mall at Port Vell called Maremagnum. It opens everyday and it is very popular.
4) If you are interested in modern architecture, that what it remains from the Forum. The main building, the Photovoltaic Canopy, St. Adria Port, a beautiful park called Diagonal Mar Park by Enric Miralles,...
And about Montserrat, there is no need of a car to go. A train from Plaza Espanya and either a cable car or a rack railway takes you right there. More info at
http://www.cremallerademontserrat.com/ (English version available). There are some combined tickets that include train, cable car/rack railways, entrance to museums, and even lunch. Check the Website to see fares and schedules.