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.
已 (yǐ) = already/to stop/then 经 (jīng) = sacred book/to undergo/to endure
已经 (yǐjīng) = already
can 回家 be separated, like 回了家? or is it no way?
I think you should put it at the end 回家了
Can i put 了 in the middle? 他已经了回家。
No, because "le" has to go after the verb
Sure, but it's not obvious if the verb in this case is 回 (with 家 as an object) or 回家 (without object).
It seems reasonable to expect 家 to be the object.
Are you saying this is not the case?
Well in English 'to go home' is a fixed combination too, as if 'home' is part of the verb. It is not: 'to go to home'. It might well work the same way in Chinese.
Is le necessary if we use the word "already"?
Maybe 了 is confirming that the verb is in the past?