There are 268 miles from Barcelona to Avignon.
Yes, there are several autobuses from Barcelona to Avignon. Check companies Linebus, and Alsa.
The road distance from Paris to Avignon is 692 km. The travel time is about 6H30 by car, or 2H38 when using the TGV (high speed train link).
About 5 hours by train, according to this website: http://gospain.about.com/od/bustravelinspain/a/madrid_bustrain.htm
Barcelona has a train station, so it is possible to get there by train. However. where you are starting from (which you have not specified) may not have a station or indeed be connected to a rail network.
22h10 including night train (sleeperettes) between Barcelona and Milan.
The best way to travel by train from Barcelona to Carcassonne is to take a high-speed train from Barcelona Sants station to Narbonne, and then transfer to a regional train to Carcassonne. The journey takes approximately 4-5 hours.
To be honest, it's probably better to fly, but if you want to take the train, you will need to take a train first from Barcelona to Venice in Italy. Then you will need to take the train from Venice to Vienna.
The travel time from Barcelona to Lisbon on the high-speed train is approximately 10 hours.
The best way to travel by train from Barcelona to Lisbon is to take a high-speed train from Barcelona Sants station to Madrid, and then transfer to another high-speed train from Madrid to Lisbon. This route offers a comfortable and efficient journey with beautiful scenery along the way.
The trip will be approximately 18 to 22 hours.
Not directly, you'll have to change twice.