As of you:
Adam was warned when he was in Jannah.
Adam was warned in Jannat because he was a mortal being then. At that time, He was awaiting the Day of Judgement so He had to do good deeds and about bad deeds He was to be warned. The deeds of this world will be rewarded there and then there will be no warnings because that Jannat will be of the hereafter life. It is a common misconception that Adam was in jannah. Yes, He was but not in jannat of His deeds rather it was a temporary location for him and He must had to follow the rules there.
And as of you:
Will we be free in Jannah or will we still be under the threat of punishment?
You have got Jannat already by your deeds and due to earthly warnings so there are no more warnings over there. You will never be under the threat of Punishment.
Allah states in Quran. Surah Az-Zukhruf Ayah no. 68:
[To whom Allah will say], "O My servants, no fear will there be concerning you this Day, nor will you grieve,
So, there will be no fear, tear etc.. then my brother!!!