If i have a character with a certain ability that increases as I level up, does it increase if I cross-class or prestige class?
Example: a Breaker Barbarian with the Battle Scavenger special ability
"Battle Scavenger (Ex): At 3rd level, the breaker barbarian suffers no penalty on attack rolls when using an improvised weapon or a weapon with the broken condition. In addition, she gains a +1 bonus on damage rolls with improvised or broken weapons for every three levels beyond 3rd. This ability replaces trap sense."
and at the appropriate time, I decide to prestige to a stalwart defender. Does the ability increase with my level or does it stop when I take my first level of the prestige class?
99% of the time you lose a class features progression if you go into another class or PrC. One of hte only examples of an exception is the Oracles curse, which has half progression outside of the oracle class.
That said, working with your DM about this might be nice. Talking about things goes a long way, and if he doesn't think its overpowered why not eh?
Ideally, the ability will state "class level" or "character level."
If it states "class level" (or specifies the class, such as "sorcerer level" or "cleric level") then multiclassing or prestige classing will not advance the ability. Ex. Sorcerer bloodline abilities
If it states "character level" then ALL levels, from ALL classes, are used to advance the ability.
Many abilities just say "level," without specifying. This should normally be read as "class level."