For example, if the perk says "Damage Bonus vs. Undead: High", does that mean every weapon has this damage bonus?
If the Swift Steps II perk says "Speed Increased: Medium", what gets increased exactly?
If the Grounding III (shield icon) perk says, "Increased Shock Resistance: High", does that apply just to my shield?
Damage bonus vs. MonsterX is used for all of your weapons.
MSI, much like the MSI on Mercurial, Mercurial Demo, and Black Kat Kowl is on your knight, despite it showing on weapons.
I should test if it works for the shield with Purity l. SHIELD WITH CURSE RESISTANCE FTW!!!!!
Sprite perks apply directly to your knight. In practice, this means that every weapon you have gets that damage bonus high vs undead. Swift Steps is MSI, as Skyguarder mentioned. It makes you run faster and you will find this extremely noticable if you have other MSI gear available, such as Black Kat and Mercurial.
Grounding doesn't affect your shield at all, it affects yourself. This is the same way armour works. When a piece of armour has 40 defence, it makes you take 40 less damage when you're attacked. It's no different from wearing a wyrmwood bracelet (except the sprite perk gives a much higher bonus). The icon being a shield is a visual shorthand for the perk being defensive.
Damage Bonus vs Undead High means your weapons are more effective against the undead.
Swift Steps means your movement speed. It's not ASI.
Same thing for Grounding lll. I'm assuming that your helm, armor or both get some resistance.