In Pathfinder, and all 3e derivatives, "one class has nothing to do with another." Really, "one level has nothing to do with another" either - you add on the extra stuff for that level without much complication.
So yes, if you have two different classes, you get the bonus spells for each class, and get to cast spells chosen separately for each class. (So yes, with orisons, if you are clever you'd choose different ones). This is balanced by multiclassing almost always being a suboptimal deal in Pathfinder; they largely eliminated the "multiclass always good" and "dips aplenty" problems of 3.5. And one of the reasons for this since you ask, caster levels from different classes (regardless of arcane or divine) do not stack unless you have a feat or power that specifically and explicitly allows them to. So you could take one level in 4 different divine spellcasting classes and have a stunning number of orisons and level 1 spells, and pretty good saves, but you'd definitely be behind a "real" fourth level character.
As I read it, you're half right: the spell allows you to make multiple touch attacks (as an exception to the basic rule of "one touch attack per casting"), which means that you're effectively holding the charge until you are either out of targets or do something else which would dissipate the charge.
I say "half right", because casting a spell immediately dissipates the currently-held spell. So, if you cast Chill Touch again, the first casting would dissipate.
As I read it, then, the round in which you cast Chill Touch, you'd get one free melee touch attack with which to touch your first target. In the following rounds, you could make further touch attacks as standard actions, until you've succeeded on as many such attacks as your granted by your Caster level or until you cast another spell (noting that touching something that isn't strictly a target would use an attack; eg, using a two-handed weapon would hit the weapon with a charge from the spell).
The basic rule: Touch Spells in Combat
Holding the Charge: If you don't discharge the spell in the round when you cast the spell, you can hold the charge indefinitely. You can continue to make touch attacks round after round. If you touch anything or anyone while holding a charge, even unintentionally, the spell discharges. If you cast another spell, the touch spell dissipates. <snip> If the attack misses, you are still holding the charge.
Best Answer
No, it doesn't stack
This has been answered in a FAQ:
This includes the spell Death Knell, spell-like abilities that cast Death Knell, wands of Death Knell, and magic items that have the effects of Death Knell.
Although the FAQ is about temporary hit points, the principle is that bonus from the same source should not stack, as described on the Core Rulebook, under Combining Magical Effects.
Even when an effect is not labelled as a "bonus", if the effect increases it, it is gaining a bonus. Just like the spell grants you bonus temporary hit points (normally you have 0).