Can mortgagor sell mortgaged property while pending suit for recovery?

There are many questions in your query but I understand that the theme / circle / boundary is only one question which is as follows:-

"You have sold some property which was already mortgaged by some bank."

Answer:- The bank can file a suit for recovery of funds and if those are not recovered or cannot recovered then and only the bank can pray to the court for possession of the property or to recover their funds by selling the attachment (property itself).

Basically the bank only needs funds, no matter how you do that, no matter you repay the loan by selling the mortgaged property. The onus will lie on the purchaser as whether they have checked the property value or any sort of loan running on the property.
 

In one way, if the bank has given the loan to purchase your property then it has the share on your property but banks cannot ask for their share to property but they can only ask for their funds, this can be explained by the below mentioned example:-
 

If the property value is 45 lakhs and if you have taken the bank loan of 15 lakhs only, so in common man's language bank has 1/3rd share but it is not like this. If after 5 years the property value becomes 90 lakhs then you will have to pay the banks those 15 lakhs+their interest and nothing else, bank cannot ask for their 1/3rd share for about 30 lakhs after those 5 years. 
 

If the bank files suit for recovery of funds but if you sell that property while pendency of suit and you get 90 lakhs then you can very well repay bank loan, bank and court will have no objection to that but you cannot highlight yourself that you have done this as this is not allowed till you get the no objection certificate from bank and why the banks would give you NOC to sell the property as bank will never know the increased property value. 

Your next question's answer is:-

If a person sells the property vide G.P.A to other person while the property is mortgaged with some bank and the G.P.A holder further sells off the property vide sale deed but the bank funds are still pending on records then bank can very well file a suit for recovery of funds but they don't know about the 3rd party who purchased the home, banks can very well ask for recovery of funds and if not recovered then banks can sell off the property through bank Auctions which is also called Foreclosure and the purchaser of the house / property will have to bear the losses, it is thus advisable for any purchaser to conduct proper title check from registrar office.