2. What do the numbers of the skills even mean? Is it like GURPS where there's a percentile roll under the skill number? If so, what does 200 skill points do that 100 doesn't?
I’m not an expert, but yes I believe it is GURPS-like, ie your skill values are nominally on a 100% basis. What >100% gives you, or really just high values in general, is the ability to overcome significant maluses to your roll. For weapon skills this is related to lighting, range, weapon str requirements, opponent dodge/evasion, and any debuffs you may have. This generally holds true for stealth too, with the addition of competing vs enemy detection.
For technical skills like LP, H it’s just that the dynamic range goes above 100. The only malus you may encounter is due to debuffs. Conceptionally, for these skills and persuasion intimidation chemistry mechanical etc, the effective challenge ceiling is a bit under 200 and values over 100 just represent increased difficulty. I think styg did it this way because it made balancing skills easier by keeping a common skill point pool. If non-combat skills only went up to 100, they would need a distinct SP pool to reflect the increase value per point.
Well, skills are not really GURPS-like... There is no difference between values below/above 100. Skills are just flat numbers that nominally increase by 5 each level for the PC and NPCs alike. It's a linear system that could be scaled up to any arbitrarily high value for skills and levels. Relative power of characters is checked in calculations involving 2 actors and PC-only skillchecks are roughly level-based, with high base ability scores allowing the player to outpace the level curve.
Combat skills and some others are compared against the adversary's skills.
Attack/defense skill ratio is the core of the calculations, but higher skills often also help overcome other modifiers on top of the skill ratio like agris pointed out.
Ranged/aoe attacks vs evasion, melee attacks vs dodge, stealth and pickpocketing vs detection, trap detection vs traps, resolve vs mental debuffs and fortitude for physical ones. Those derived stats are basically just auto-leveled skills. You can't accidentally over-invest in combat skills since damage-dealing skills always increase your damage and you would have to be far above enemy skills to hit the cap on random rolls. Basic (skills only) calculation for ranged & melee precision ->
https://underrail.info/junk/precision.html
One-sided skillchecks (dialog checks, crafting, lock opening) reflect the level of the content/zone, but that's not a strict rule. The devs adjust skillchecks to whatever they feel is appropriate. 5 skill points a level plus 10 extra points at first level. That's the basis of all level/skillcheck balancing.
