What is the purpose for constructing shrines? Is it lawful to visit them? Is not fasting for a whole lifetime and not praying also or fasting and praying the Maghrib and Asr Salah in the shrine worth it to keep the person in the grave happy?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Constructing shrines, distributing food at them, praying at them or making I’tikaf and similar forms of worship at these places is forbidden.  It is an innovation that has nothing to do with the true religion.  The Prophet (Sallallahu Alaihi wa Sallam) forbade constructing buildings on graves and ordered to flatten the graves to the level of the ground.

So, it is mandatory upon the Muslim to avoid indulging in such innovations and to warn other people against such myths and superstitions which lead only to polytheism and to seeking help and protection from other than Allah.

For the second part of your question, know that fasting regularly is a highly praised act.  However, giving up praying is an obnoxious one.  The person who gives up praying is even considered by Shariah (Islamic law) as a Kafir (disbeliever) or even Mushrik (polytheist).  Some Muslim scholars are of the opinion that the person who gives up praying goes out of Islam, hence fasting or other good deeds will be of no benefit for such a person. 

So, if you know this person, you should advise him/her to repent sincerely and inform him/her that to give up prayer is Kufr.  May Allah guide him/her to the right path!