I thought, I could copy commands from the info panel put them to a *.py file and run them like I could do in a MEL script. Seems not.
How can I execute those functions sequentially from a python script by pressing ALT+P on the text file ?
In any script, the first thing to write is "import bpy". Once you have that, you should be able to copy/paste from the info editor like you've described.
Does that fix it?
It may also depend on what commands you're thinking of - some areas of Blender are easy to copy from the info editor while others can be weirdly cryptic.