How to best execute the same query on many different vector layers?

You can use the "Execute as Batch Process" function the Sextante Toolbox provides.

It's easiest if you first define a new Model based on the MMQGIS Select tool using the Sextante Modeler to fill in the parameters:

After saving the model, you can right-click on it in the Sextante Toolbox and select "Execute as batch process". In the window that opens, click on the ... button in the Input column of the first row, and select all your vector files using Ctrl or Shift (you choose from the file system, not the Layers list). In the first row of the Output column, enter a file name for the output. After you've chosen the first file name, a window will pop up asking you if you want to auto-fill the other Output names. Choose "Fill with parameter values" to base the output file names on the input file names. After closing the pop-up, you just have to press OK to run the batch process. The selected features will be written to the specified output files.