'Turn' has specific meaning, and means all of your turn, four clicks, beginning to end (or of corp, your mandatory draw and three clicks). Putting a Virus counter on Crypsis will cost you a click, but the virus counter is not lost until either you remove it (because you used Crypsis to break at least one subroutine during an encounter) or the Corp purges virus counters. If you still have virus counters on Crypsis at the end of your turn, they stay there.
As Frybender has pointed out, Strength-boosting lasts for a single piece of ICE unless stated otherwise - not a turn, not even the duration of a click. So if you boost Crypsis to break a Wall of Static, then encounter an Enigma, Crypsis meets Enigma with Strength 0, forcing you to spend to raise his Strength again if you want to use him to break the Enigma. Crypsis' dependency on virus counters, and constanly resetting to 0, makes him more expensive than say, Gordian Blade, but Crypsis is more versatile has he can break ALL ICE he ecounters (provided you have enough cash/virus counters).
The lins in the rulebook saying 'Agendas can always be advanced while installed' means that AS LONG AS an agenda is installed, you can take an advancement action. It DOESN'T mean that you can take an advancement action AS PART OF an install action.
Edit: I'm sorry, that probably reads as overly lecture-y. Welcome to Netrunner, I hope you enjoy
Edited by CommissarFeesh, 14 October 2013 - 10:35 AM.