Can a changeling say they want to transform their arms into one race, change their legs into another, and then change their face into a different race or person. Can that be done? Does their transformation require concentration while they maintain their form?
Yes, you can look like parts of different races if you want.
You decide what you look like, including your height, weight, facial features, the sound of your voice, coloration, hair length, sex, and any other distinguishing characteristics. (Wayfinder's Guide to Eberron)
The changeling's ability gives them the ability to look however they want as long as you appear the same size and general shape. And appearing like another race even in just an arm is simply a matter of cosmetics (color, texture, characteristics, etc). With no other restrictions put in place, it is completely up to you what you look like and nothing preventing different parts of your body from looking different from each other.
The changeling's ability does not require concentration since it is not a spell, but you do revert to your original form when you die.