"Do you think I can remove the portafilter gasket, clean behind the shower screen and put the gasket back or will I need replacement gasket? My machine is in very good conditon and don't think it's been used much, so feel a little uneasy to remove the gasket."
You'll need to remove the gasket from time to time to service the machine. If it's still flexible you should be able to gently pry it out. If not it's probably worth getting a couple so you have replacements on hand.
"I don't think my machine has a pressurestat, there is no copper pipe under the base? Should I still bleed air out of the machine?"
No pressurestat, but that's perfectly OK. I have one where I installed a modern heating element with pressurestat and two that I restored with the old two element heating system. I like the old style as much as the new.
"I turn on machine on hi setting, after 7min 20s there comes few drops of water out of safety pipe and after 7min 50s steam comes vigorously through safety valve."
That's exactly as it should be.
"With 14-15g dose I get max 24g output with single pull and stock basket. How much output should I be able to get with this setup? So far only low volume and bad tasting shots but I am anyway in love with this lever and hope things get better with practise so I can retire the Silvia."
You need an excellent grinder to properly control a pressurized manual lever machine. Beyond that it's practice, practice, practice. The coffee cake is the brakes of this car. With the mediocre shots you might learn to enjoy milk drinks while improving technique. The truly bad shots of course go into the sink. After awhile you may not need to measure anything and the shots will be consistently good. With new coffees you may take a couple of shots to dial in and the others go to milk drinks. At least that's where I am these days.
If you're not familiar with it we on Team HB consider the following required reading for this site. If your eyes are bleeding it can wait until at least tomorrow morning. Espresso 101: How to Adjust Dose and Grind Setting by Taste