Well no one could reply but after getting experience let me explain this myself:
Question 1, Answer: The 5 berth compartment does exist. The usual saying that there are only 6 berths is wrong. There are 5 berths at both ends of the coach (might be 1 in some, but Khyber Mail 2Down had 2x berth compartments), it will definitely be cost effective for someone wanting to personalize full cabin for family in 1 berth lesser fare.
The veil however covers only half of the cabin (as the veil's railing ends at the curve of the last compartment). Still one can easily manage to put their own veil as i did for complete privacy.
Pros of 5 berth compartment:
1. Cost effective for small family of up-to 5 (or 6 with small kids).
2. Much easier for loading and unloading the luggage.
3. Bathroom access is very easy, specially useful for kids.
4. Much Better privacy.
5. Lesser interference even though the door is adjacent.
6. Front area is not crowded, only 1 seat with no berth in-front of the cabin,
7. People's / kids noise only 1 sided.
8. Side with 2 berth has much better space.
Cons of 5 berth compartment:
1. No fan, although not really bad as the AC's are already chilling. But troublesome if AC unit fails even for sometime, keep a small portable fan or the hand blower in case.
2. Frequent disturbance from door, but if you don't care, its ok.
3. Might cause a bit more disturbance if your side is towards the engine if the coach is attached next to engine, but i did not have this problem fortunately, usually the lower AC is not attached with the power van.
5. Water shortage after every 1-2 hours. It had to be refilled 3 times during the whole journey, needed to wait for refilling stations and had to preserve water in bottles. The reason is that the Lower AC coach is very crowded.
Question 2, Answer: Not really evident regarding this, it was not present as i did not see it, all i saw was 5 berth compartments at both ends, the railway's online display of coach's berths might be wrong regarding this. The people say the 3 berth might exist like a room with door but without any window.
Regarding my last question of Khyber Mail: It is also Ok, but i experienced much better quality in Karachi express. Also the AC of Khyber mail Lower AC Coach failed in the first 1-2 hours, sweating us to death, i had to take my kids in business class passageway to recover during that time, the staff was very cooperative tho. Even afterwards the AC could not really chill the coach, the evaporators were constantly blocked by ice, and the AC also got tripped due to daytime temperature, only at night time it became ok. So it has newly upgraded coaches but service quality is still questionable, their claim is vague, Khyber mail or other cheaper ticketed train's Lower AC is not recommended. Only the business class and AC-sleeper AC was perfectly chilling.
In summary, I went UP in Karachi Express AC sleeper, the best experience, perfect, no complain at all, infact you can shutter off AC unit if it is extra chilling (only found this option in karachi express out of 4 trains)! Unfortunately could not book Karachi Express AC sleeper in time for return. The khyber mail and other trains i tried like jaffer express (tried it's ac sleeper from RW-LHR, the electrician turned off AC with no evident reason, he presented a vague excuse that he turned off AC for kids as it chills a lot, but even afterwards he turned ON only 1 unit of AC out of 2 in the 4 berth AC sleeper, weird service, train quality was also low and some facilities lacked like call button did not do anything, light's problem, no dust bins, no hand-wash, water leakage making it all drained slowly etc as compared to Karachi express...), not up-to the mark.
Karachi Express AC-Sleeper is the best cabin in the whole railway service, even 2 berth AC Sleeper is much better for your 4 member family with 2 small kids, very comfortable, peaceful, clean, fully private, no interference at all and full time high quality service, and also the evening - noon train timings are also the best.