Shaking @ 30 psi = foam (unless you have some experience with this and know about how long to shake). Shaking @ 10 psi would accomplish the same thing without the danger of overcarbing.
Yes, you want to leave the beer line attached all the time. The usual carbing and serving pressure is around 10-12 psi. At this pressure, it cannot overcarb. Unfortunately, however, your beer is already overcarbed due to the shaking. To fix that, turn off the gas and pull the pressure relief valve several times over the next day or two to bleed off CO2 from the beer. Once you get foam free pours, turn the gas back on to 12 psi and leave it there. If after a couple of weeks at 12 psi you decide it can stand some more carbonation, raise it another 1 or 2 psi and wait a couple more weeks.