Some more theory
To get from philosophy into something more useful...
The Coriolis force is always proportional to the speed of movement - faster - more coreolis (see it as a reversed g-force when making a turn of same radius in different speeds). A faster wind "turning" to align with a pressure gradient will theoretically need a stronger force than a slow wind to keep "on track". (Remember the force was invented to explain how the wind stays aligned with the isobars.)
It might get stronger in your book because sometimes the explanation of the wind theory starts from stillstand - when the air speeds up the coriolis increases - with the speed. The more important issue is that it also changes direction to aways keep at right angles with the movement - why - because thats how the force is defined. This causes a spiralformed "start" of the wind until it is aligned with the isobars.
With regard to the rest im not completely sure what you mean but i will give it a try.
To get geostrophic wind you need a straight airflow/isobars (otherwise there becomes more forces involved) where the Press Grad F and Coreolis F can equalise. So no friction and no curves otherwise the theory doesnt hold (In either case the wind doesnt follow those rules.)
The speed of the geostrophic wind is dependent on the latitude with stronger winds at low latitude. (Compare two similar pressure gradients on different latitude without any other change. ) Not at the equator though because there doesnt exist geostrophic wind there (how - technically the earth doesnt rotate there it only moves sideways = no coreolis) There still exists wind there but it needs another explanation so it is conveniently named into something else.
In the geostrophic case there is really neither a Low or a High only lower and higher pressure which decides the direction of flow (together with earth rotation)
If you speak about the difference of wind around circular high and low pressure centers we need a more complex solution which includes the forces induced by the turn or to keep circulating around a center. This is not completely geostrophic wind anymore.
To explain this we need one more force or just change the value of any of the other two, for example add a centrifugal force and depending on the direction of turn this force will either add too or subtract from the pressure gradient force. If it is additional this means higher windspeed in the end and vice versa. In the case of air circulating around a high we have an addition (both hemispheres since both the direction of the wind and the direction of earth rotation reverses) this means in practise that around a high pressure center the wind will be stronger compared to a low pressure center with the same pressure gradient and shape. (remember to keep all the other factors constant)
Or more commonly - when the wind turns to the right it increases in speed(northern hemisphere) and to the left decreases.
If you want to combine many factors you need to start calculating but that is not really needed at this stage ;-)
So concentrate on how not why and keep it simple and you will nail the exam.
Have fun