Yes as you were not convicted. Your attorney that did a great job for you could have answered this as well.
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The short answer is "yes." But you should get a certified copy of the docket showing the case was dismissed. You never want to rely upon the accuracy of a background check. If you have the certified docket handy, then you will be able to show it to a prospective employer quickly.
Yes, you may. But perhaps if the charges imposed against you were unreasonable to have been brought in the first place, you may able to file a petition for factual innocence which would clear your arrest record, if, you were actually arrested as well.