سارح in Egyptian Arabic has two meaning s and both are somehow related .First it means walking for a long distance usually a farmer walking down to his farm or shepherd going after his animals(سارح =shepherd in standard Arabic) or some street vendors carrying their goods to different places.From the previous example s they all walk for long distance.Now,back to the song مهما كنت في غلطك سارح means no matter how far youve gone down the road of mistakes,no matter how much off track you are, every thing is going to be ok.The second meaning of سارح is when someone is not concentrating" cause too many thoughts are going through his mind so his mind is walking away with these thoughts and thats how it relates to the first meaning.So,الليل طويل مليان احلام تاخدك و تفضل فيها سارح means Night is long full of dreams that will take you in a journey ( your mind will walk for long down the road of dreams).Hope its all clear by now.

It means dreamy or absent-minded.

سارح ..it means wondered off

In a first place, I would say that سارح is related to "free, to liberate, to let (it) go". Considering that سارح is coming from the word "سراحة" which is related to freedom. If I'm wrong, maybe someone will correct me. Hope it helps though :)