I can only answer some of your questions, you never really mentioned what form of travel your doing, motorbike, car, pedal cycle or public transport?
The best time to travel through Pakistan regarding weather is from September to May. From May to August you can travel but it will be really hot and humid and depending on where you are in the country there will be ablot of monsoon rain. Its not that it cant be done but its maybe a little more effort Is required.
You can drive independently after leaving Boulichistan region but levies/police sometime escort you all the way to Sukkur, it all depends the on the situation In the region and if the levies/police have the resources. Usually up until Quetta you get an armed escort and once you leave the quetta region your pretty much on your own or vice versa up until Quetta your okay and then you need armed escort up until the border to Iran.
The security situation in Pakistani is constantly up and down, one minute its all peaceful and the next massive expolisions, the region you will be passing to get to Iran border suffers from terroisim mainly because there are allot of Shia Muslims living there which are constant target by the Taliban so you could be at the wrong place at the wrong time. If your a westner then easy option is keep a low profile and you should be ok. Just travel during day light hours and with an escort and you should be ok.
What is a LOI?