Question
Hi, hope u doing well. I belong to northern areas of Pakistan.

1. My vine has been suffering from "ant infestation". The ants are bigger ones "black asian ants". they crawl up the stem part of the plant till its fruit and also damage it.
Another thing, a white substance can also be seen associated with these ants in the stem where i presume the ants feed or has been developed by ants.

2. I have some pomegranate plants in my garden too. The problem is that when the fruit is about to ripe, a tiny hint/hole appears on it which would later on spread into the fruit and destroys it, makes it rotten from inside .. eventually making it fall from the plant.

What to do ?

Answer
Problem 1.
The white substance on the vines that is associated with the ants is probably aphids, scales or other insects.  These insects will suck on the vines and are the reason the plant is suffering.  When the insects feed, the produce a sticky substance called honey dew.  Ants love it!  The ants will collect the honeydew and will actually protect the insects that produce it.  I would suggest treating the vine with an insecticide to kill the other insects and it is likely that the ants will leave.  It is also possible that the vine itself is producing the sticky stuff from some sort of wounds and that is what the ants are collecting.  You will have to take a closer look, possibly with a magnifying glass to try to see what sorts of critters are there.

Problem 2.
The hole sounds like it was created by an insect.  Maybe a pomegranate fruit borer (or it could be a similar insect).
http://ip-pest.ucdavis.edu/index/pomegranate-fruit-borer
The females will deposit their eggs in the small pomegranate fruits and the borer is developing inside and eating.  When the larvae matures into an adult insect (in this case, a moth/butterfly), it will make a hole to exit.  This is probably the hole that you are seeing. The internal part of the fruit is already damaged, but it may get worse now that there is an opening.  Some other bugs or mold fungi may get in through the wound and make it worse.  You will have to treat for the insect if you want to have good fruits.  The link above has information on what products to use and timing of application.

Good luck!