Transportation from Lijiang to Lugu Lake

1;2;4: Yes, there are private cars to the lake from the old town. It costs about CNY 600 each day. One day is not sufficient. Generally speaking, you need to spare two days, so the fare would be around CNY1,200.
3. Yes, it may take about 7 hours to reach the lake due to the poor road conditions.

Also, you can travel by public transport. Take a coach to the lake from Express Passenger Transport Station at No. 933, Shangri-la Avenue. The coach is scheduled at 8:30 every day.