Q:

Is it necessary to keep a cat's nails trimmed?

I have a six month old cat.
The problem is here are too many stray dogs and they kill cats. So I think letting my cat having sharp nails will give her advantage if it comes to fighting with a dog for life.
I do get occasional cuts but I can tolerate it as long as my cat is well prepared for danger.
But does the cat herself face any problem with big nails like problem walking?
Also there are not too many things at home where my cat can scratch nails to keep them at size. 

A:

Indoor Cats
Most people will cut their cats nails to prevent damage to furniture, children or other pets in the household. 
Young Cats will maintain their nails by themselves through scratching and do not require trimming unless for the reasons above.
The exception would be defective claws or "mittens"

Cats have a much harder time maintaining these nails as sometimes they come out deformed or wedged too closely in between toes. These should be checked regularly as they can grow into the paw pads, this is painful and if untreated ends up with infection.
Senior Cats need regular checks as with arthritis developing in their joints they cannot keep those nails nice and tidy. We see these types of nails often in our senior cats (pictured below) as most people do not know.

As you can see this is very painful and will cause problems walking. You can check out this answer on helping senior cats manage arthritis. Wikihow has a very good article on trimming nails.
Outdoor Cats
Outdoor cats need their nails for defense so I do not recommend trimming if she goes outdoors. With the exception of problematic nails. 
Choosing the Right Scratching Post
A scratching post should be taller than a fully stretched cat for optimal use, there should be more than one and each with different textures.

Cardboard
Carpet
Sisal rope

Spraying or sprinkling catnip on the posts or cardboard will entice your cat to use them instead of your furniture.

