1. My family moved to Australia when I was 10 years old.
2. My family moved to Australia while I was 10 years old.
(Can we use 'while' as in #2?)
3. When will you come to my house?
4. While will you come to my house?
(Is #4 wrong? 'When' is an interrogative adverb? What about 'while'? Is 'while' an interrogative adverb or not?)
2 and 4 are incorrect.
"When" is an interrogative as well as a conjunction; "while" is simply a conjunction (or a noun, if used as one).