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Your olives won't develop a single trunk on their own. To develop a single trunk, you need to prune out those branches at the base.

It depends on what zone you are in and the variety. Most olives are very cold tender and need to be brought in in the winter. To be on the safe side, we would say that if you live in a zone lower than Zone 9, the tree will need to be brought indoors.

The best time of year to do this would be early spring. Any soil that is rich in compost and organic material will work well. This article will also help you avoid transplant shock, which can happen when repotting: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

As long as the stems are still alive, the trees can recover. The best thing that you can do with them is to just give them a little extra TLC. Trees that are more stressed are more likely to get pests so keep a sharp eye out for a possible pest infestation and treat it as soon as possible if you see one start.

There is a sterilizing treatment that can be applied to the tree by a professional arborist or lawn care specialist (it is not available to the public). It is not 100% effective and needs to be applied yearly, but will significantly reduce the number of olives the tree produces. Here is more information: https://www.gardeningknowhow.com/ornamental/trees/tgen/fruit-tree-sterilization.htm

It all depends on what cultivars you have. Many olive tree cultivars do not fruit until they are 5-12 years of age, however, there are some cultivars such as 'Arbequina' and 'Koroneiki' that fruit as young as 3 years old. And, most olive trees need a pollinator tree of a different cultivar (are both of your trees of different cultivars?). There are also non-fruiting cultivars of olive that never produce.

For more information on growing olive trees, please visit the following link:
https://www.gardeningknowhow.com/edible/fruits/olive/olive-tree-care-information.htm