In the beginning of October I want to make a little bicycle trip in Finland.
Is it possible to stay with a tent in Finland? Or maybe available some areas where you can make a camp for free?
Certainly, there are lots of campsites in Finland.
Even better, Finland has the concept of 'jokamiehenoikeus' or freedom to roam, and :
"One may stay or set up camp temporarily in the countryside, a reasonable distance from homes, pick mineral samples, wild berries, mushrooms and flowers (as long as they are not protected species)."
What you might need to consider, however, is the temperature in October, depending on where you are. Up north in Rovaniemi, for example some might find it quite chilly to be camping or cycling.