I guess, in a way you are right. If you use defeat as a verb, the subject of the sentence (in an active sentence) is winning. Example: "The king defeated the rebels." (so the king won). If you use defeat as a noun, it usually means the instance of being defeated. Example: "The defeat of the rebels had great impact on the country." I hope this clears it up a bit! Good luck!

No. You are confusing who is defeating and who is defeated. If team A defeats team B it is also true that team A hands team B a defeat.

No. They have the same meaning.