I have noticed there has been a gap developing between house perimeter and concrete. Can you please suggest how can i fill this and what would i require.
That's an expansion joint which needs to be there. The gap looks about right to me, and I would be hesitant to suggest you fill it with anything. There shouldn't be any reason to worry about this gap as it prevents your bricks and concrete slab from cracking.
is it ok for water to go through brick and concrte. Although the slope of the concrete is towards other side just wanted to check.
It's fine for water to run down there. The concrete slab level would be below the damp course layer in your brick wall, and the water will disperse under the slab.