Learn English – “Whole Wide World” , “Whole World” , “World” Any Difference

"By far and wide" is simply an inappropriate mixture of "by far" and "far and wide".

The speaker or writer has gaffed, or has picked up the usage from someone.

"By far" is used to express a degree to which something is superlative. If something is by far the best, it means that the distance between that thing and the second best one is conceptually far.

"Far and wide" is an common phrase which refers to a conceptual or physical two dimensional area (which has width and depth).

"The king looked far and wide for a bride".

"By far and wide the best" makes no sense, because comparisons are arranged on a conceptually linear scale, not a two dimensional scale.

I would recommend new learners of English not to use this: keep "by far" and "far and wide" separate.

Broad and wide are synonyms and can usually be used interchangeably. They are both adjectives for a horizontal dimension.

In your example it is most likely being used metaphorically, it conveys the idea of a military commander surveying a battlefield and taking into account everything that is happening at the periphery, to left and right, as well as at the centre.

Taking a broad view is certainly idiomatic, perhaps clichéd.

Large is different, it can be applied to a variety of dimensions and quantities. It doesn't have the same connotations.