So the max level is 50, which means there is 50 perks right?

And the max level for each skill is 100, but after 100 it's a lot harder to level them up?

The level most people will comfortably reach is 50. You can gain levels until all your skills are 100. That level in somewhere in the 70s, though I have heard as high as Level 81.

The thing is, the higher a skill is when you gain a point in it, the more it will contribute to leveling up. The lower a skill is (relative to all other skills) the less it contributes to you gaining a level.

For planning purposes, just assume level 50 is the max and plan accordingly. That means 49 perks (you start at level 1), and I have heard there are 20 perk points you can earn through quests. But don't hold your breath for those. I've been playing 70 hours so far, and I'm level 40, and I haven't found one of those quests that rewards me with a perk point yet. So they may be out there, but don't plan on them.

You start at level 1. The soft level cap is 50. This is where you stop getting perks for every level, and where level advancement and skill progression becomes slower.

Skills can be raised to a maximum of 100. Fortify enchants/spells can make them temporarily higher than 100, but you cannot advance them past 100.

Absolutely wrong. Not only do you still get perks, but if you didn't, it would cease being soft.

My apologies then, I misunderstood the definition of the soft cap. It was my understanding that 49 was the cap for perks from levels, and that there were additional perks available from quests.

Generally, a soft cap means that all leveling features continue, but there's no experience available to level with. It's a prohibition on leveling placed outside the actual leveling system.
However, when there's respawning this is meaningless. The devs generally use it to mean that they didn't design any content for past that point.