You can cast a spell at a lower caster level than normal, but the caster level you choose must be high enough for you to cast the spell in question, and all level-dependent features must be based on the same caster level.
Take it with a pinch of salt, but this is as best an explanation: you can't cast a spell if the caster level is lower than the norm. Thus, you can't cast a 1st level spell without having at least 1 point of CL, and CL is, like most of the stuff in D&D, rounded down. So it'd be zero CL at 1st level, CL 1st at 2nd level, CL 2nd at 4th level, CL 3rd at 6th level, and so on. Unless you specify such, you need a minimum caster level to use the spell; hence, if you intend to keep the progression of spells as-is, you wouldn't be able to cast 1st level spells until CL 2nd (because that's the moment when a paladin gets to cast 1st level spells), or until 2nd level when you get your first CL. Likewise, you wouldn't be able to cast 2nd level spells until you got CL 3rd (which means up until you get to your 6th level in Paladin) OR until you get to 8th level (when Paladins get to use their 2nd level spell slots). And so on.
To clarify: to cast a spell, you need at least three things:
- At least one spell slot to prepare (or available, if able to cast spontaneously)
- The minimum ability score to cast the spell (in this case, a Wisdom of 10 + spell level)
- The minimum caster level to use the spell. In this case, a Paladin can cast 1st level spells at a minimum CL of 2nd, 2nd level spells at a minimum CL of 4th, 3rd level spells at a minimum CL of 5th, and 4th level spells at a minimum CL of 7th
Regarding this last bit: a Paladin would get, as mentioned, its first actual CL at 2nd level if going half-caster; CL 3rd at 6th level, CL 5th at 10th level and CL 7th at 14th level (notice the pattern?). Thus, you wouldn't be able to cast 5th level spells until your caster level reaches 9th, which is achieved at 18th level.
IIRC, Mystic Ranger grants full spellcasting from 1st level, including full caster level. If it grants half, it's a great deal of misunderstanding from Paizo and the designers, because the rules specify you need a minimum caster level to use the spell. In essence, when you reduce your caster level, you are casting the spell as if you were a spellcaster of a lower level; otherwise, if you had no restrictions based on CL, you'd be capable of casting a 9th level spell if you had a 9th level spell slot. Notice the wording of Precocious Apprentice; without the requisite caster level, you couldn't use that 2nd level spell slot, but the feat allows you to ignore that. As a bare minimum, you cannot cast a spell of a specific spell slot if your caster level is lower than (2x-1), where X is the level of the spell you intend to use.
Thus, you need to change that at the very least, because most 1st level spells require you to at least have a caster level of 1st, which you couldn't have unless you gave full CL or fix that so that you can do so.
Finally: in my glossary, "caster level" refers to that number that determines range, duration and sometimes effect of spells; "spellcaster level" is the effective level in the class that grants you spellcasting ability; "spell level" is the number that determines the DC of the spell plus the grade of power of the spell (with 0 the lowest and 9 the highest). Three different things.
It's not so that you take it bad or that I don't seem to understand it (though the petition to clean up the table a bit is so that others do), it's on the rules and all I'm doing is giving ideas on how to tweak it to get what you want from the class without having troubles with the core rules of the game (because a 'brewer always has to respect the rulebooks, you know, unless your intention is to splinter from them).