Welcome aboard, Herr Kaleun.
This will answer most your questions - your hydrophone works only when submerged, so your "sonar guy" cannot report anything when on the surface.
As to the ships - yes, they should dissapear when "No God's Eye" is ticked.
Sigurd answered correctly about the "third option". Also remember, that your sonar guy will never be as good as you are in hearing things. However his efficiency will grow as time passes. Give him a "sonarman" qualification and he will be much better. Always try to keep the green bar over your sonar room as long as possible - the longer the bar is, the better the efficiency (applies to all other rooms as well).
I'd say do not fear to set your realism to 100% at once. It could be a bit difficult at start, but with the help from community you'll do it. You can find vast amounts of knowledge here, as well as some EXCELLENT, MARVELLOUS, ASTONISHING mods, like GWX. The difference between clean SH3 and SG3+GWX is like the one between pushing your wooden cart and riding your Ferrari.