I did 2 trips to karachi from Lahore last year by road and another the year before. Since you are travelling in January so there is going to be small daylight i.e 6am to 5:30pm i.e 11 hours and its not recommended to drive in night in january. So the best bet is to stay at Rahimyarkhan. It will take you around 10 hours from Karachi and it is around 650kms from Karachi. Well travelling in Sindh is around 600kms and it will take around 9 hours because of poor roads after sukkur and just before sukkur. Well the rest house in Rahimyarkhan is Shelton guest house and he charge 2000rs per night. It is opposite to Post office and is a nice place. Its approximately 10kms away from highway. During my 3 visits I have found RYK as the best because its almost centre point.
While coming from Sindh avoid QaziAhmed bazaar always take its bypass it would be on your opposite side while coming from Karachi. Qaziahmed is almost centre point between moro and hyderabad.
Regarding route to Multan when on N-5 you will see a board that says straight for Khanewal and Lahore and left for Multan. Take the route to Multan and head straight to Vehari Chowk the distance is almost 60-65 kms in between you will cross a round about and a railway crossing. Vehari chowk is a 5 sided round about and when coming from Lodhran you have to head in the side adjacent to you i.e suppose the side from Vehari is no 1 than you have to skip 3 sides and head towards the 5th one. Go straight on that road and you will bypass Multan and enter N-5. Its almost 20 kms from Vehari Chowk Head towards Left and keep moving towards Lahore. Take most bypasses and there is board for everyone. While returning from lahore 2 bypasses will confuse you 1 is Sahiwal bypass i,e on the left side and other is Karachi morr on entrance of bhawalpur.
Fog condition in Punjab is unpredictable my friend and you have to keep your fingers crossed.
Brother tell me which car are you travelling in and number of passengers.
I dont recommend eating enroute beacuse of following reasons
It breaks your momentum and wastes a lot of time
It is unhealthy at some places
What I do is take some home made stuff like sandwiches or rolls or pizzas everything home made. Make them hot in microwave and keep in a hotpot have it at around noon time. Try to leave at around 6am from Karachi thats the best bet and try to be patient on road.
If you need any further guidance inform me. I shall be greatly obliged to help you
