I had to switch off all of my logitech force feedback settings and to let the game do everything. I am still getting a little shaking, but turning up deadzone and turning down force feedback environmental effects helped.
I've just had a word with the handling team here and for Logtiech wheels the profiler is set to 100, 0, 0, 0. Then in game I can't remember all the settings but most set to 100 then FFB/Weight set to 50-70 depending on preference. As you go higher with the FFB you'll start to lose the nuances of the FFB effects as you saturated the motors in the wheel.
Obviously this is just the settings they've been using to setup the FFB curves for the game so you'll need to tweak some settings for your personal taste. I know for me I like a very aggressive turn-in so I can dive bomb at apexs without too much movement but that makes it awkward for longer corners.
How do you get the warm up lap on in career mode?
Off the top of my head it should be in "race settings" during the load screens between sessions, you can tweak most of the race weekend settings there. If the race event has already loaded I don't think you can enable the warm-up lap, but you can during Practice, Quali etc