Which legal action can take by company if we don't pay or serve the notice period

HI, Hope can any give good suggestion on below situation. Situation is: Person: He has joined in company A and left after 20 days. He has received half month salary not even one month full salary. He has a agreement that he has to serve notice period of 3 months otherwise need to pay 3 month salary but employee didn't signed on any physical paper he just sent email as accepting the offer. Person did not officially sent any mail as resigned from the position but sent email to HR like unable to continue due to personal issues. Later HR replied like you have to serve notice period of 3 months or 3 month salary. Person replied to HR like he can serve notice period but not immediately, can serve notice period after 6 months once issues are sorted out. HR replied like you've been terminated, need to serve notice period after a month otherwise legal actions will be taken. Q-1: Once company said you are terminated, does employee has to serve notice period or pay 3 months of salary ? if employee doesn't need any relieving letter/experience letter . Q-2: Does company can take legal action against to employee, if yes what would be the case and what will happen if we go to court? Q-3: Will it impact on employee IT career in any other organization? Q-4: Do we need to pay amount immediately or after few days/months if court has to pay employee to employer ?