I understand that seudah shelishit needs to be started before shekia. If one is only having mezonot and not bread, must one stop eating before shekia as well? In other words, can you only continue seudah shelishit past shekia if you said hamotzi?
You are correct. Well put
If you started shalosh seudos with bread before shkia, but then run out of bread after shkia, can you continue eating the non bread food at the meal? Salads, chips, soda, etc.
yes. but you should eat a kazayit.
Additionally any and every time you wash you should make sure to eat a kazayit, and should not speak till after you have consumed it. And Yes, you may eat it with other foods, it does not have to be eaten straight.
So if you eat mezonot before shekia, then you need to stop eating or drinking after shekia? The only exception is if you washed and ate bread before shekia? Just clarifying that hamotzi is the only qualifier to continue eating or drinking past shekia on Shabbat afternoon
Correct, except that eating and drinking are not the same. Water, and by extension water based drinks (coffee,tea etc) can still be drunk even post shkia, as they may be drunk prior to Havdalah. (as opposed to before Kidush when even water is forbidden)
Do you mind citing the source for allowing drinking prior to havdalah?
שולחן ערוך אורח חיים סימן רצ"ט