The title is actually a different question than the post, which contains several questions, but I'll answer all of them since they are closely related.
Why are optically active compounds abundant in nature?
Nature needs some kind of complexity to work. To build a living system you need hundreds, thousands or even millions of different molecules, just a few won't do it. If you just draw random molecules you'll end up with a lot of chiral ones. Unless you are sticking to linear chains without functional groups or aromatic (flat) systems you will almost always end up with chiral molecules. It actually would be surprising if there would be no chirality.
Given that many optically active compounds are extracted from nature, why do organisms go through pain of seperating enantiomers for their consumption ?
As Zhe already said in the comment: they don't need to separate those. All the animals and plants basically use only one enantiomer.
Why do optical isomers are found in nature that are hard to seperate in a lab?
Well, you are right. Enantiomers have the same physical properties unless they are in a chiral environment. Organisms on earth are able to produce only one enantiomer because the whole environment is chiral which means both enantiomers have different physical properties.
If we want to separate enantiomers in the lab we are using the same system. We take a chiral phase for chromatography (those are quite expensive) which means both enantiomers behave differently.
We are also able to synthesize enantiomerically pure compounds if we use a chiral environment during synthesis. But this is often expensive and we aren't nearly as good as biological systems doing this.