mathof wrote:Many Italians have the same view of caring for their mokka pots

True that, and boy what horrors have I encountered. At least I know where not to drink a coffee.

As for the OP:
Apart from soaking with cafiza or the like, soaking in hot water might help soften the old gaskets. If you wanted to push the screen out I find it safer to loosen up the lever only from the piston rod but leave it connected to the grouphead. Then you can put for example a piece of wood between the piston rod and the lever and use the lever to push down. Works wonders.

If ever would you want to / need to remove the sleeve, throw the grouphead into freezer for 30min or so, then try and remove the sleeve. Worked for me.

As for dirty screen I basically resolved that issue with the puck screen or paper filter on top of the puck. Need to clean the screen a lot less now.