They use current players. And the two competitions occur during pretty much the same time period. For premier league teams, there is Premier League games, Champions League/Europa League, FA Cup, and the Carling Cup (League Cup.) The games are just scheduled around each other. This is part of what makes European league seasons much more grueling than MLS. Sometimes three games a week. Fifth place in the league qualifies for the next season's Europa League except for this season. It will be fourth place Tottenham.