Does the ring grant complete immunity to Detect Thoughts, Discern Lies, and Detect Alignment spells, or is there a caster level check involved since it uses Nondetection to create the ring?
The spell or spells used to make an item have no bearing on the effects of that item (except for things like scrolls, wands, potions, and staves, which duplicate spells.) It works exactly like the description of the ring says - you are immune to those things.
As another example, look at the flaming weapon property. You can use either flame strike, flame blade, or fireball when making a flaming weapon. Yet the effects of flaming (1d6 fire damage) don't match any of the spell effects. You don't do 1d8+5 points of fire damage like a flame blade would do. The flaming weapon doesn't explode in a 20' radius ball of flame like fireball, nor does a flaming weapon create a 10' radius 40' tall column of fire like flamestrike.
The spells used as a prerequisite have no real effect on (most) magical item effects.