Why don't we use 完？
完 means to complete, finish (doing) something. You can't use it here
it's surprising though to a beginner. did complete going home.
can 回家 be separated, like 回了家? or is it no way?
Can i put 了 in the middle?
No, because "le" has to go after the verb
已 (yǐ) = already/to stop/then
经 (jīng) = sacred book/to undergo/to endure
已经 (yǐjīng) = already