The last question is easy to answer: 議論 is closer.
The character 討 carries a connotation of “battle”. 討論 certainly assumes there are opposing sides and possibly also that there will be a winner. For example, a debate between heads of political parties is 党首討論.
議論 is a more general term for discussion. Being a word of Chinese formation (kango), it has a formal sound to it, but it basically means the same as 話し合い when it refers to a concrete occasion where multiple people actually discuss something.
議論 can also be used in a more abstract sense, corresponding to the second definition of “debate” in the following excerpt from New Oxford American Dictionary. (The first definition corresponds to 討論.)
debate | dəˈbeɪt |
noun
a formal discussion on a particular topic in a public meeting or legislative assembly, in which opposing arguments are put forward: last night's debate on the Education Bill.
• an argument about a particular subject, especially one in which many people are involved: the national debate on education | there has been much debate about prices.