I'm playing on Creative mode and am planning to build a farm, so I plan on using spawn eggs. If there are already animals in the world ( spawned naturally) do I have to kill them all before I use the spawn egg? Or will they not have an effect?
The use of spawn eggs ignores most of the checks for whether something should be able to spawn somewhere. In particular, no check is made for amount of mobs already spawned. You can use spawn eggs to create hundreds, thousands, or even millions of mobs in an area; the only limit will be the processing power and memory needed to handle them.
There is no mention of the spawn limit on the Spawn Egg page, and no mention of a Spawn Egg failing to create the desired mob (due to that limit).
Additionally, I know from experience (and online images) that it is possible to create vast farms (that would override the maximum for passive creatures).
Thus, your spawn eggs should perform as expected.
No, there is no limt on how many animals that you can spawn. Althouth if you spawn too many on a slow computer you may experience some lagging, etc.