Pronunciation of 和 in Taiwan
As recorded in Baidu, this unique pronunciation of “和” as "hàn" actually originates from the Old Beijing dialect. Extracted from the blog article titled 台湾人为嘛把“和”读作hàn?, it says the following:


  1945年10月台湾光复，日语的“国语”黯然退出，台胞急着要回复祖国的语文，要说国语，要认汉字。
  1946年4月2日台湾省国语推行委员会正式成立。台湾国语会的标志性贡献是编订《国音标准汇编》，作为推行标准国语的根据。1946年5月1日起，由“老北京”齐铁根先生每日在清晨7时，在电台担任“国语读音示范”，播讲民众国语读本、国语会话，国民学校国语、常识、历史、各种课本，供学国语的人收听，匡正语音。当时的学校教师现听现学现教，使广大的学生也能及时学到国语，学习标准的国音。这位齐铁根当时成了家喻户晓的大师级人物，直到现在上年纪的台湾人还能回忆起齐先生娓娓动听的“京片子”，连词“和”读hàn（“汗”）就此在台湾深入人心。


In short, a Mandarin Promotion Council was formally established in Taiwan after the end of WWII to restore the literacy level of the Chinese Language. Mr Ji, an old-timer from Beijing, was enlisted to do a daily national broadcast to demonstrate the standard pronunciation of Mandarin through a series of dialogue and reading sessions. The teachers learned as they listened and help spread their knowledge to the students. Mr Ji was widely regarded as a Mandarin guru at that time and he is still a familiar household name for many of the older Taiwanese today.