Termination from office

Dear Sir/ Mam, I have worked with this company for 2 months as Senior Executive - HR. One day as usual I was travelling to office but reached late due to trains delayed because of unexpected heavy rainfall in December. I had also informed my colleague (immediate superior) about it via what's app. which she approved. As I reached office, I was asked to go back home by our Director since I did not reach in time. I couldn't even punch for the day. Before I could even react, I left immediately since I couldn't face other employees because I was ashamed of myself. The same day (6th December) I resigned via mail informing the Director and HR about travelling issues I was facing but they asked me to serve one month's notice which I agreed to and replied to them on 7 th December and was ready to go to office next day. But to my surprise, on 7th evening they informed me that I need not come and my dues will be settled. I was OK with it but when I checked my Fnf status they told me that I will be paid only for the number of working days and Relieving letter will not be provided. Instead the will issue me a termination letter. I do not have anything in writing from the company about the whole matter. Everything was via phone. Now my question is: 1. Can the company issue me termination letter? 2. Am I not eligible for a Relieving letter? 3. Shouldn't the company pay me one month's notice pay?(which they claim is not applicable as per Appointment letter)