White Algae? Wow!! I think my problems are moving into a new course? But thanks a lot Ben, its a lot of help just identifying the problem itself.

So, what is white Algae? Yes, it looks like calcium carbonate , when I squeze it, it just turns to powder and dissolves. I tried to test it, but could not test with certainty. I tried to scrub the wall with the diluted acid solution, just like you told, but when I put in the pool, I can not really determine if it frizzes and dissolves.. may be the sponge gets drenched in pool water and makes the acid very diluted.
I have this quite a lot in the pool bottom I think. When I brush specific parts inside the pool, a lot of brown powdery substances come up and some other places its white powder..My filter doesnt seem to be catching any of these stuffs.. I dont know if my filter is working well or not!

I attached a picture of the pool wall and the whitish cloud that comes up when I brushed the side.. please let me know your thoughts, Thanks!