Do the following three sentences mean the same thing, that is, can they be used interchangeably?
In this case, they can be used interchangeably as each one of them means "and". Here are the minute differences:
与 [yǔ] is more elegant and formal and is usually applied to similar items of abstract and contrasting nature. E.g. 天与地 (heaven and earth), 是与非 (yes and no).
和 [hé] is more general and informal and can be applied to list dissimilar items and more often on objects. E.g. 汽车和现金 (car and cash), 蓝宝石和翡翠 (sapphire and jade).
跟 [gēn] is used more often in speech and is usually applied to similar items and more often on humans. E.g. 他跟她 (he and she), 我跟你 (you and I).
跟 is totally oral and informal. The other two can be used in both formal and informal situations although in oral conversation 和 is more common. A person who speaks 与 (together with other formal/"classical" words) too much may be considered fastidious and/or pedantic.
They have the exact same meaning. Other than a formality, people pick the one that is easy to pronounce and sounds smooth. For example, 英语与法语 is hard to pronounce so people may prefer 英语和法语; on the other hand, 战争与和平 sounds better than 战争和和平.
When connecting words with "classical feeling", such as one-character words, 与 is used even in oral language, e.g. 学与玩. In this case, 学和玩 sounds okay but 学跟玩 sounds somehow unnatural.
But again they mean the same and are interchangeable. It's only about tone, feeling and idioms.