most important thing you missed is, do you have your own transportation or do you have to use public transport? Even if you have your own transport, you will just be able to hike upto rush lake and back in Lahore in 7 days time, if you go by air, then i guess you will have 2 days spare as the trek to tush lake is of 3 days depending on the route you take, some routes take 3 days to reach the lake and 2 days to return to hoper village meaning 5 days, some take 2 days to reach the lake and 2 days to return. So i guess you just need to focus on one thing only.
As for security situation, this is the main concern but as it is said " is tara to hota ha is taraha ka kamo ma"