Does "got used to" mean the adjustment is still happening?

No. "Got used to" can describe a completed change: "I eventually got used to the shared kitchen." "I'm getting used to it" describes a change still in progress. The form of "get" tells you where the process stands.

Does being used to a task mean being good at it?

It tells us that the task is familiar. Experience may help someone do it well, but "be used to" doesn't itself mean skilled, successful or happy about the task. Read any extra information the sentence gives you.

Home Grammar Used To ExercisesUsed To - Real-World Contexts Exercises

Used To - Real-World Contexts Exercises

B2-C1 Level

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Read what each sentence says about the person's experience: a former routine needs used to + base verb; something familiar needs be used to + -ing; becoming familiar needs get used to + -ing. The workplace vocabulary changes, but these meanings stay the same.

I'd check the words before the gap next. After couldn't or take time to, use get; for a change completed in the past, use got. Some repeated actions in a clear past setting also allow would. Follow the particular situation, even when several sentences share a workplace theme.