Some sourcing and then my interpretation. Am I reading this correctly?
School abjuration; Level bard 3, cleric 3, druid 4, paladin 3, sorcerer/wizard 3
Casting Time 1 standard action
Components V, S
Range medium (100 ft. + 10 ft./level)
Target or Area one spellcaster, creature, or object
Duration instantaneous
Saving Throw none; Spell Resistance no
You can use dispel magic to end one ongoing spell that has been cast on a creature or object, to temporarily suppress the magical abilities of a magic item, or to counter another spellcaster's spell. A dispelled spell ends as if its duration had expired. Some spells, as detailed in their descriptions, can't be defeated by dispel magic. Dispel magic can dispel (but not counter) spell-like effects just as it does spells. The effect of a spell with an instantaneous duration can't be dispelled, because the magical effect is already over before the dispel magic can take effect.
You choose to use dispel magic in one of two ways: a targeted dispel or a counterspell.
Targeted Dispel: One object, creature, or spell is the target of the dispel magic spell. You make one dispel check (1d20 + your caster level) and compare that to the spell with highest caster level (DC = 11 + the spell's caster level). If successful, that spell ends. If not, compare the same result to the spell with the next highest caster level. Repeat this process until you have dispelled one spell affecting the target, or you have failed to dispel every spell.
For example, a 7th-level caster casts dispel magic, targeting a creature affected by stoneskin (caster level 12th) and fly (caster level 6th). The caster level check results in a 19. This check is not high enough to end the stoneskin (which would have required a 23 or higher), but it is high enough to end the fly (which only required a 17). Had the dispel check resulted in a 23 or higher, the stoneskin would have been dispelled, leaving the fly intact. Had the dispel check been a 16 or less, no spells would have been affected.
You can also use a targeted dispel to specifically end one spell affecting the target or one spell affecting an area (such as a wall of fire). You must name the specific spell effect to be targeted in this way. If your caster level check is equal to or higher than the DC of that spell, it ends. No other spells or effects on the target are dispelled if your check is not high enough to end the targeted effect.
If you target an object or creature that is the effect of an ongoing spell (such as a monster summoned by summon monster), you make a dispel check to end the spell that conjured the object or creature.
If the object that you target is a magic item, you make a dispel check against the item's caster level (DC = 11 + the item's caster level). If you succeed, all the item's magical properties are suppressed for 1d4 rounds, after which the item recovers its magical properties. A suppressed item becomes nonmagical for the duration of the effect. An interdimensional opening (such as a bag of holding) is temporarily closed. A magic item's physical properties are unchanged: A suppressed magic sword is still a sword (a masterwork sword, in fact). Artifacts and deities are unaffected by mortal magic such as this.
You automatically succeed on your dispel check against any spell that you cast yourself.
Counterspell: When dispel magic is used in this way, the spell targets a spellcaster and is cast as a counterspell. Unlike a true counterspell, however, dispel magic may not work; you must make a dispel check to counter the other spellcaster's spell.
The General Rule for Caster Level is as follows:
Caster Level
A spell's power often depends on its caster level, which for most spellcasting characters is equal to her class level in the class she's using to cast the spell.
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.
In the event that a class feature or other special ability provides an adjustment to your caster level, that adjustment applies not only to effects based on caster level (such as range, duration, and damage dealt), but also to your caster level check to overcome your target's spell resistance and to the caster level used in dispel checks (both the dispel check and the DC of the check).
Other entries state:
Caster Level: Generally equal to the number of class levels (see below) in a spellcasting class. Some prestige classes add caster levels to an existing class.
Caster Level: A spell's power often depends on caster level, which is defined as the caster's class level for the purpose of casting a particular spell. The word “level” in the short descriptions that follow always refers to caster level.
Just below is the example given in Dispel Magic.
For example, a 7th-level caster casts dispel magic, targeting a creature affected by stoneskin (caster level 12th) and fly (caster level 6th). The caster level check results in a 19. This check is not high enough to end the stoneskin (which would have required a 23 or higher), but it is high enough to end the fly (which only required a 17). Had the dispel check resulted in a 23 or higher, the stoneskin would have been dispelled, leaving the fly intact. Had the dispel check been a 16 or less, no spells would have been affected.
My reading of the example is that it implies that Stoneskin and Fly were either cast from two different sources, or for some reason the same caster chose to lower the CL when he cast Fly. Stoneskin is a 4th or 5th level spell, which means its minimum Caster Level is 7th, but by the example and based on the definition of Caster Level, a 12th level Sorc/Wizard/Druid cast it. Fly is a 3rd level spell, which means that its minimum Caster Level is 5th, by the example it was cast by a 6th level Sorc/Wizard.
Is there such thing as a minimum Caster Level? Can a 10th level Wizard intentionally cast Fireball at CL 1, doing only 1D6 damage, consequently lowering that Fireball's CL to 1st? Would it's counterspell DC via Dispel Magic then be 11 plus 1 = 12?
As for using Dispel Magic to counterspell, by my reading you must Ready an Action to counterspell against a specific target, and once that target begins to cast, you cast Dispel Magic. At this point, you add your Caster Level to a D20 result, and then compare that to 11 plus the Caster Level of the spell being cast. If you meet or beat that result, you've countered it.
All that sound right?
A. You can intentionally lower your caster level for a spell you cast, so long as it doesn't go below the minimum caster level required for casting the spell (Example: A 10th level evoker casting Fireball can lower the caster level down to 5 and do 5d6 damage, but no lower).
B. Correct on the counterspell, except for the part that when the target casts a spell, you must make a Spellcraft check to identify the spell. After that, you either have to cast the same spell as the target or cast Dispel Magic (Or if you have the Improved Counterspell feat, you can cast any spell from the same school of magic as the target's spell).
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Well technically yes there is such a thing as "minimum Caster Level"...the answer is IN the quote you had from PRD
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.
so no you cannot cast Fireball at CL 1..its a 3rd level spell so the minimum caster level to cast it is I think 5th (maybe 6th, i dont play casters much) so if you were 10th level wizard you could cast it as no lower than CL 5th