ignazthecat top group valve is completely worn out should not be chamfered. It is the reason why you can’t get water out of the group properly and needs either the cam follower replaced, or preferably the entire valve., as it’s seal will probably be in need of replacement as well.
using the last photo, the middle valve is the preinfusion valve and should not have a spring on it…This I have highlighted in yellow in the photo
Lower valve is the vent valve and should have a spring..as in the photo..the spring you have on the preinfusion valve should be on the top valve and the spring on the top valve should be on the vent valve. It might be why the top valve wore so much
P.S. Preinfusion valve may have a worn cam follower as well. Contact AC S for a spares pack, see if they can send it as a small packet of some kind.
P.P.S. You need to lubricate the group after backflushing with cleaner and periodically.
http://coffeetime.wikidot.com/e61-lubrication