Actually, it's not "easy".
You can use those two expressions, too. The meaning is almost the same. The last one から focuses more strongly on the "reason/cause" than していたら or していて, though.
The main function of the -te form is to connect clauses in the temporal order. The meaning differs depending on the relation between the clauses, so it might be just "and", or it could be "so" just like in that case.
The subject of the first clause is interpreted as "she", thus, it means "because she went to a room, she wasn't here/there(= this "here/there" is not the room, of course)."
You mean
行っていたら, right?
This is "contrary-to-fact in the past" as the same meaning as 行っていたなら.
This is invalid. 間に indicates a temporal point in a period, so it should be 部屋に行っていた間に、彼女がいなくなった。. Notice that いなくなった is an action, unlike a state いなかった.
It's "while/during" vs. "and then". 駅にいたとき is more common for the former, and the latter can be "contrary-to-fact in the past"; もし駅に行ったなら、お母さんに電話しただろう (i.e., the speaker actually didn't go to the station and didn't call their (or someone's) mother on the telephone).
I already explained it partially in your previous thread.
The meaning differs depending on the type of verbs "punctual or durative", since the meaning of the ~ている form differs depending on it (on-going action vs. present state resulting from the past action). Have you already learned ~ている form?