OK - I'm gonna take a quick stab here, as I think this post isn't quite a duplicate of some of the other Golden Ratio or Fibbonacci questions... here we go!
1) I use a set of Golden Ratio / Fibbonacci overlays when I design logos, and sometimes even page layouts, websites and other graphic design layouts (I have also used this concept pretty broadly in my other life, as an architectural designer, where its use is quite common, and is still taught in many architectural schools) and these are how those overlays appear:
These can be overlaid on photos, or on design blank sheets for guidance in initial ideation - the use is multivariate and as individual as the designer is.
The basic idea of a proportioning system is to connect the proportions (ratios of relative sizes) of your design elements (whether those are graphic elements on a page or display or an array of columns in a garden or the decorative details wrapping around the bases of engaged pilasters which frame and form a building portico) to some over-arching concept to give your design visual consistency. This proportioning system, or its use can be entirely arbitrary, or may synthesise a naturally-based system and an arbitrary system (Le Cobusier, I'm looking at you & Modulor) and may be of limited use for any specific design task, or may be of great assistance.
In the case of using Fibonacci and Golden Ratio systems, the goal is to connect your design's proportions to more broadly observed, understood and recognisable proportions from nature. The Fibonacci sequence of numbers gives rise to the Fibonacci spiral, and the Golden Ratio gives rise to the Golden Rectangle. If you nest Golden Rectangles, you get the Fibonacci Spiral (the spiral's curve passing through one intersection point of the implied squares when you nest two Golden Rectangles), and if you fill each implied square with a tangent circle you get a Fibonacci sequence of circles - A.K.A. Golden Circles. This was all based on attempts to codify human and other natural proportions going back to Vitruvius & Alberti in mathematical terms and expressions - today we might add our understanding of the concept of fractility to this toolset (the degree of brokenness, roughness or bifurcation of an entity expressed as a ratio with its length or volume) but for the usecase of simple graphic design, it would perhaps be overkill.
The most effective point in the design sequence to use a proportioning system is early ideation through design development - by the time you're getting to real hardlines, you're really too far down the pitch for these concepts to be useful; moreover, as already mentioned, these are typically used as a guideline and starting point versus a specification or standard, though if you've been rigourous in apply these ratios you can use them as an element of your QC at the end of your design process.
I can tell you that in the world of architectural design, these ratios and ideas are not only still in use, you can experience for yourself their unconscious impact by traveling to a building designed when the use was more common (Italy, Sicily, Greece, France, Spain) and you are likely to be able to feel the difference in your experience of those buildings in comparison to most latterly-designed buildings.
Though there are indeed many who happily (and often loudly and aggressively) eschew any use of such "antiquated" systems, often decrying them as "B.S.", there is also ample evidence (much of the more recent stuff based on A/B testing and other similar prejudgement-neutral testing) that the non-design-trained general public simply responds more positively to, for example, logos designed using such systems, feeling them to be more professional, more pleasing, more subtle, more solid - the descriptives are legion, as are the experiences - in architecture, we might say that there is an ineffable experiential quality brought by simple proportionality, and that despite both its seeming challenges of application to more current building system approaches and its potentially arbitrary nature, its lack is always self-evident and definitive. That is to say - you may not know when a design is proportional in a pleasing way, but oh boy do you know when it isn't.
Here are a few commonly-touted examples of the use of Golden Ratio and Golden Circles in well respected and recognisable logo development:
And one just 'cos I think the flow is lovely and so illustrates that designs using a proportioning system don't have to be static or stiff:
Now - to be super-clear here: using a proportioning system, whether Fibonacci or other is neither de rigueur for good design, nor is it a garantor of success - this next image shows a grid-based logo in process which I think quite strong, and I don't see an explicit proportioning system at play in this image:
All that said, I think that this previous question (though not a direct duplicate) will be of use to the OP and others trying to understand the mechanics of use of proportioning systems in graphic design:
How to use Fibonacci numbers / Golden Ratio in logo design in Illustrator or Sketch?
Hope all this helps you some.