They Repel.
You then have two balloons in very nearly the same place.
The balloons would repel each other due to like charges. Like charges repel each other according to the principle of electrostatic force. This is because the negative charges on both balloons create a force that pushes the balloons away from each other.
When a charged balloon is allowed to touch a neutral balloon, some of the charge from the charged balloon will transfer to the neutral balloon. This transfer of charge will cause both balloons to become slightly charged.
The force between two balloons would be due to electrostatic forces, as the balloons can become negatively charged and repel each other. The force would depend on the charge of the balloons and the distance between them.
They would be strongly attracted to each other. Multiple such attractions are what hold together solid sodium chloride.
If you rub two identically charged objects together, they will repel each other due to like charges. The objects will not stick together and may even push each other away.
-- There is a force of attraction between them. -- If the charges were big enough, a spark would jump between the balloons and equalize the charges. -- That would require a huge charge, so there's no spark. But if you allow the balloons to touch, then electrons eventually flow from the negative one to the positive one, and the charges equalize.
They would be charged
Because it did.
If each balloon were given the opposite charge, the balloons would attract each other instead of repelling. They would come together and possibly stick together, forming a cluster or a chain depending on the arrangement of the balloons in the original photograph.
If you touch a positively charged electroscope with a negatively charged object, electrons from the negatively charged object will flow into the electroscope. This will neutralize some of the positive charge, causing the electroscope's leaves to collapse or move closer together. The extent of this effect depends on the amount of charge transferred during the contact.
The water balloons will remain intact but will reach the same temperature as the cooler. If the cooler is cold, the water balloons will also be cold. If the cooler is warm, the water balloons will also be warm.