Aquorys

I guess the best answer would be "it depends...", but generally speaking, an AMRAAM does not care about your aircraft's lock. AMRAAMs are guided via datalink and their own onboard active radar homing equipment in the terminal phase. The guidance equipment uses the most recent information about the target's position and movement to find the target, meaning that if a target's position and motion are plausible, based on the most recent information received on the datalink and the time elapsed since then, it will lock onto that target. How this works in detail, e.g. the exact distance/speed/direction tolerance based on a certain scenario, is classified information, therefore, there is virtually nothing you can do to figure out whether the behavior of the missile was realistic in DCS (outside of signing up for a job at Raytheon 😂).

Sounds normal and realistic to me. The flight control system does not auto-trim for roll, and trim is virtually never perfect. I'd rather say that roll trim being perfect with a balanced loadout, until you touch it, is a DCSism, as you called it.

Check the caution lights, the safe way to start is to wait for the SEC light to go out before moving the throttle to idle.
PS: Also, see the checklists linked in my signature, in case you are looking for something that you can put into the kneeboard as a quick reference.

Did you boresight it?