How can income distribution and direct transfer payment be used to reduce inequality and poverty?

Be serious. Taking money from one person to give to another is robbery, even when it's done by a government. It always INCREASES inequality and poverty. But there are always plenty of dingbats who think they can make it work somehow.

Go to www.mises.org and read the free materials about economics. Go to www.fee.org and read the free materials about government, and the site will offer you some free ebooks.