Probably the hardest task that I have to face is shooting at midday, when the sun is shining strong. It seems that whatever I do, the image does not look good. It looks burned. I tried After Effects to fix it, without success. 

I believe the issue might be my current lens, which may or might not be adequate for outdoor shooting. I am open to suggestion regarding which lens should I choose. Is there a company manufacturing these special lens?

You can use a sun filter, but the most affordable option is to shoot at the right hours, not at midday.