Go with Mary, chat with Chinese people, 'with' here actually is 'and', Mary and I went to the store. Those Chinese people and I are going to have some talk. So you could use '和'. e.g. 我想和中国朋友聊天. 我和Mary一起去商场.
With a can opener, 'with' here is: Using a can opener, I openend it. So you use 用here. 用is a verb. e.g.我用剪刀把信封拆开.