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This can be hard to say. These will spread and close together no matter the distance. The closer you put them together, the faster they will form wall. If you want to have a few years in between pruning, then you may need to plant them 3 or 4 feet apart.

Here is an article that will help: https://www.gardeningknowhow.com/ornamental/cacti-succulents/prickly-pear/opuntia-barbary-fig-plant.htm

Yes, you can remove the old Figs.

You can leave them in hopes of ripening. This will not harm the tree. If could be that they are not getting fertilized, unless this is a self fertile variety. Here is an article that will give you more information on their care: https://www.gardeningknowhow.com/edible/fruits/figs/how-to-grow-figs.htm

Those are a type of scale bug. These will destroy your tree if left untreated. I recommend neem oil as long as you do not apply it in direct sun. This article will give you more information: https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm

This looks like minor accumulation of salts from watering and fertilizing. It is not a fungus and should not affect your fig. Make sure you are following instructions for fertilizing. A switch to demineralized or filtered water will reduce salt accumulation.

Your fig tree should be old enough to bloom, so there is likely an environmental issue going on. This article might help you find the answer:
https://www.gardeningknowhow.com/edible/fruits/figs/fig-tree-is-producing-fruit.htm

Here are some more general reasons a plant may not bloom:
https://www.gardeningknowhow.com/plant-problems/environmental/plant-not-blooming.htm