Not that you did anything wrong but, I always long soak and scrub new equipment in PBW. Then rinse hot several times followed by a star san rinse. Star San will sanitize but isn't a stand alone cleaner. New equipment can be pretty dirty.
Since you already pitched, I would not worry about the rate and just give it extra time to finish. Next time, take a gravity reading before you drain your kettle and add some boiled top off water until your gravity drops to where you want it. Your ABV will be higher with the higher OG, but not a...
It's not from sitting on the trub. 3 weeks or 4 weeks would not be to long. 14 days may not be long enough but is a minimum for me. Sitting on the trub would have no effect on off flavors after such a short period of time. I would concentrate more on possible cleaning procedures.
For racking off of dry hops in a carboy, I have been using this on a stainless racking cane for several years and it works great.
I always use whirlfloc and cold crash. They come out crystal clear and are a summer favorite by everyone who has it. The longer you can cold condition it (Lager) at around 34F, the better it will be. Last year, I had one in cold storage for 6 months before tapping and it was great.
Use a standard racking cane and a carboy cap (double spout type). Tilt the carboy while racking. After cold crash, I have very little beer left behind, maybe a cup. I personally don't like the auto siphon as it is difficult to suspend off of the trub.