1. What do the Horizontal and Vertical sync pulse values do and should I even touch them? They also seem to move automatically when I change porch values.
These are pretty much standard so there's little point in touching them. They are taken from the ntsc tv standard, so they're guaranteed to work on 100% of standard resolution CRTs.
2. When carrying the front and back H porch values to the mame.ini, should I also carry the pulse sync (since whether I touch it or not it seems to change)?
You can do it but I wouldn't bother unless you're getting very different results between Arcade OSD and GM, due rounding errors.
You see them changing because all values are interdependant, so when you change any of them the others are recalculated.
3. Is it possible to adjust vertical centering in the mame.ini or are all vertical geometrical changes impossible through software? If centering is possible how does one go around with the values as a percentage of the values from the existing mame.ini values or just putting in the arcade osd values even if mathematically they are not balanced to the default values in mame.ini?
Yes, vertical centering is possible. And it works in a deterministic way with arcade monitors, but not so well with TVs, because these already have circuits to center the picture that mess with our settings.
What you need to understand about vertical porches is that what you specify in there are the
minimums. Based on that, GM/VMMakier will add as much blanking lines on the top and the bottom as required, in order to meet the horizontal frequency set by you in the crt range. E.g., if 12 lines are required, it'll add 6 on top and 6 on bottom. If an uneven number is required, one porch will have one extra line compared to the other.
Now let's say your picture is consistently shifted down. What you need is to add some extra lines to the front porch. Instead of using Arcade OSD, just take your crt range and do the simple maths:
0.191 is the default sync pulse, we know it stands for 3 lines, so one line equals 0.191 / 3 = 0.0637 ms.
So if we have this crt range:
crt_range0 15734.26-15734.26, 59.94-59.94, 1.500, 4.700, 4.700,
0.191, 0.191, 0.953, 0, 0, 192, 240, 448, 480
The front porch is also 0.191, let's add one extra line to it: 0.191 + 0.0637 = 0.255. So:
crt_range0 15734.26-15734.26, 59.94-59.94, 1.500, 4.700, 4.700,
0.255, 0.191, 0.953, 0, 0, 192, 240, 448, 480
You'll go on adding lines until the problem is fixed.
If the problem was the opposite, we'd increase the back porch. Notice we want to always increase any of the porches, we never operate by decreasing.
4. Lastly when in arcade osd as I adjust for geometry and get close to the desired geometry I generally start seeing wave patterns of faint lines generally moving left or right, and as I make changes it changes the direction or intensity of these interference like patterns. Sometimes If I ignore geometry and just try to move porches back and front for the sake of reducing the interference I'm able to get to a point where interference seems to disappear altogether. Are these related to the sync pulses and do I need to care about it when calibrating for the mame.ini?
This is your TVs fault, unfortunately.
I'm leaving a lot of questions but I really want to learn and understand how this works better but the tutorials I've read mostly explain the basic usage of Arcade OSD and I'm unable to find answers to these.
That's the good attitude. I'd say a basic standard res arcade monitor is better for learning purposes than a TV. Of course arcade monitors have their own problems. But TVs tend to behave randomly to the untrained eye, due to this undersired centering they perform.