Q. Shalom Aleichem Harav!
If one eats and does melacha before havdalah without having said baruch hamavdil (and forgot to say atoh chonontanu) what are the consequences? is it called chilul Shabbos and does one have to daven shmona esre again?

A. Shulchan Aruch (299: 1) rules that it is forbidden to eat or drink before reciting havdala. The reason for this prohibition is not so one may not forget to recite havdala, but rather a proscription based on “yikro DeShabso” or honoring Shabbos itself, similar to kiddush (O.H. 27: 4) where we are encouraged that the first taste should be in esteem and recognition of the greatness of the day.
Mishna Berura (294: 4) writes that although we rule that if one ate before reciting havdala, he may recite afterwards, when one also omitted the havdala said in the tefila, we penalize him and he must repeat the amida of maariv and recite therein ato chonantonu. As opposed to the case if one just forgot to say it in the tefila, when he can just say the words hamavdil ben kodesh lechol afterrwards, without repeating the entire amida.
If one ate before davening maariv (after nightfall) and then also forgot to recite ato chonantonu in maariv, Poskim write that he must also repeat the amida (Piskei Teshuvos 294: n. 21 quoting Birur Halocho).
In regards if any of the above transgressions are to be called a chilul Shabbos, Horav Shlomo Miller’s Shlit’a opinion is that it does not carry the severity of actual desecration of Shabbos doing melochos during the day.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a