Please explain to me the difference between these words.

1. 防御 vs 防衛. (Defense)

2. 投降 vs 降伏. (Surrender)

3. 交渉 vs 折衝. (Negotiations. Which is more suitable for war, and for things like business?)

4. 休戦 and 停戦 seem to be the same? Both used equally often or any difference?

5. 武器 is weapon only and 武具 is "weapons + armor"?

Thank you.

See a translation

Each has almost the same meaning, but is slightly different.

1. 防御 is often used in individual subjects.
例　ナイフを使って自分の身を防御する方法を学んでいる。
Ex. I'm learning the way of protecting myself with a knife.
防衛 is commonly used in national or political topics.
例　国の防衛は重要な政治的テーマだ。
Ex. Nation's defense is an important political theme.

2. 投降 is used when soldiers in a war zone or a suspect barricading himself inside gave themselves up to the enemy or police.
例　立てこもり犯人は人質を解放し投降した。
Ex. The suspect taking the hostages and barricading himself inside finally gave himself up to the police.
降伏 is used when the war ended and the defeated country conceded defeat.
例　日本は原爆を落とされアメリカに降伏した。
Ex. Japan surrendered to America after the atomic bombs.

3. 交渉 means negotiation as you say.
We seldom use 折衝. We use it only in formal and highly business or political situations. It's an extremely polite expression.

4. It is tough for even Japanese to tell the difference between 休戦 and 停戦. We almost never distinguish between them.
If I had to say it, 停戦 would mean that the military authorities order the front to stop fighting. 休戦 would mean an agreement between countries.

5. 武器 means weapon.
武具 means old-fashioned armor. The warriors wore it before the Meiji period.