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It sounds like your fig tree might have rust. This article should help:
https://www.gardeningknowhow.com/edible/fruits/figs/figs-disease-rust.htm

Shaded areas of the foliar canopy of course cannot photosynthesize nutrients from sunlight, so foliage in those areas will yellow and decline and drop. But as long as a large percentage of the foliage can get sunlight, and other aspects of your soil fertility and water management are in order, then it won't be cause for overall decline and mortality.

Yes voles and other rodents can damage the tree. It's best to control them.

http://www.lrconline.com/Extension_Notes_English/pdf/vole.pdf

This sounds like powdery mildew. This is easily treatable. This article will help: https://www.gardeningknowhow.com/plant-problems/disease/get-the-cure-for-powdery-mildew.htm

Most fruit with some markings or spots are completely safe to eat. Without seeing the damage, I can't say for certain what the fruit is damaged from.

Transplanting of course will give you the fastest results, depending on the size of the tree, your skill and ability in moving an established tree, and ability to follow up with appropriate soil and water management as the tree gets established in it's new location.
Starting a new tree from a cutting also takes knowledge and skill in the various techniques available for propagation. And if successful, it will take a few years to become established and productive.
If you are not experienced in transplanting or in propagation, it may be best to seek professional help, to avoid failure and disappointment. Especially in the tree moving, for which you will have only one chance to get it right.