Yes, these can be interchangeable in certain contexts. However, there are some stark differences where you would use one over the others. 1) Used more so for something you're learning about/gaining knowledge about. Eg: "While I'm still learning English, I'm becoming more familiar with it." "Are you familiar with changing a tyre?" 2) This is used when you begin to think something is natural because you've experienced it regularly; particularly becoming familiar with a new situation. Eg: "I have lived in Australia for a year now and am becoming more accustomed to it." "He is becoming more accustomed to living without electricity." 3) Become aware of or familiarising oneself OR more so related to knowing people. Eg: "Sally and I have become acquainted through mutual friends." "I am not acquainted with him in any way." "We should all be acquainted with the new laws." 4) To become familiar with something or someone so you no longer find them unusual, difficult, surprising etc. Eg: "I'm getting used to driving the more I do it." "Now that she has been living with me for quite some time, I am finally getting used to her being around the house." Hope this is helpful!

Thanks a lot, Karl Thompson.

They're interchangeable, yes.