Are idioms affected by tone changing rules? For example, if I have the idiom:

一路平安

Does the tone of the 一 change to a second tone because 路 is fourth tone?
Yes it should be pronounced as the 2nd tone because it's put before character with the 4th tone. The sandhi rule applies with idioms too.

The cases 一 should be pronounced as the 1st tone, i.e. shouldn't change the tone, are listed as the follows:


  
  单独念时。如：一，一、二、三
  用在一词或一句的末尾。如：统一祖国，唯一条件，单一成分，表里如一，不论三七二十一
  表示年、月、日。如：1911年1月1日，一二•九运动，九•一八事变
  表示序数。如：第一村，第一名，第一等，第一位
  


(1. when used alone; 2. when used at the end of the word or sentence; 3. when used in date; 4. when used as ordinal number with the meaning "first".)


  “一”在上述语境中，不管它后面跟的字是什么声调，“一”的读音都保持其原调阴平，不发生变调。特别要引起注意的是第四种语境，因为许多序数在表述时采用了省略“第”的格式，这时“一”字也应读原调。


(Under the above circumstances, no matter what the following character's tone is, 一 should keep its original tone (i.e. the 1st tone) and doesn't change.)

试析“一”声调的读法