Although I have set them to appear e.g. 6 products per page this does not seem to affect the final number of products displayed in the results (even if I change this for example to 12 or something else).
Also (this may be related to the previous problem) many products appear two or three times in the results.
Finally on products ordering:
(1) The ordering with (increasing) price does not work properly showing cheaper products after other more expensive and
(2) How can the visitor check whether the ordering he has chosen will be increasing or decreasing?

Default items per listing view in Config/shopfront sets backend and frontend list length.

Excuse me but I do not understand your answer.

I konw where to set frontend display, but the settings I do do not affect the public section of the store

On which page?

Maybe you mean Configuration/Templates/Set the pagination sequence for the List Box.....

For example lokk here, please: www.auto-style.gr/gkshop2/index.php/el/ilektrika/bataries/aftokiniton

Hello,
May be, The product effect extension sp filter virtuemart. You ought to ask a third party provider
Thanks