hi Preet,
Refer the below links for your reference.
Frorm this links you can fetch and read you Email for gmail account using GMAIL POP3 mail Server.
Also if you need to add reply fuctionality to the inbox email then just add onr reply button in grid and on click of reply button try to implement below article code to how to send email to user. fro that you just need to get the FromAddress from grid row reply button click and need to set to ToAddress in popup rest you can do as Per explained in Article.
For How to use Modal popup on click of Button from Gridview row refer below article.