A disc fork can shudder because the headset is not properly tightened. It can also shudder because the disc rotor is not properly bedded in or because of uneven rotor wear. And if the brake caliper isnt properly tightened, that too will cause fork shudder(and eventual damage).
As for the handlebar setup- you do what you need to make the bike fit, but when the bars are pointing up to the sky like that it sorta makes drop bars pretty pointless since you cant easily brake from the drops. The ramps and hoods being set up flat with the ground allows for a rider to easily access the tops, ramps, hoods, hooks, and drops.
If you need the bars to be higher up and closer to you for a more upright riding position, maybe get a positive rise stem which will do both things. Or new bars with shorter reach can help too, plus there are bars with 20mm of rise from the center clamp to help get the bars up higher.
A bike that pulls into a turn more than you want could be due to a low tire. It could also be due to frame geometry you arent use to(though with you riding road and mtb, you already ride the extremes of geometry) since a gravel bike's trail is going to be higher than a road bike.
The larger a fork's trail, the more readily it will flop into a turn when you lean.
I dont know your bike's frame size, im guessing 54 or 56, but either way the Checkpoint's trail in those sizes is not high compared to many other offerings on the market right now. It would most likely be between your road and mtb.