Acoustic slinkys are fantastic strings and they'll go very well with Seagulls. 11s are lighter than what comes as standard on Seagulls (and indeed most acoustic acoustic guitars) which are factory strung with 12s. 11s will work very well for you and you may not have to adjust the truss rod at all. If you feel the need to drop to 10s by all means do so. Assuming the neck was adjusted correctly before hand, the worst that can happen is that you might get some string buzz, in which case you might have to loosen the truss rod a little, but it might not be necessary at all.
It's a very simple and non-scary job to do - looking down the neck with the truss rod nut closest to you, 1/8 turn it to the left should do the job nicely, another 1/8 of a turn if necessary. No real need to loosen the strings, but you do not want to damage the strings when turning the truss rod key so loosening them helps to keep them out the way. Re-tune and play to test. IMO, it's impossible to screw up a neck if you are only making a few small corrections. It's a shame that manufacturers and unscrupulous techs scare people so! FWIW, it usually takes me longer to find the right sized tool to do it than doing the actual adjustment itself.
Enjoy your slinkys and your seagull!