I bought my TS HD connection from Amazon in Nov 2015. It was really quick, they installed it next day itself. I don't see any trouble in purchasing it from Amazon. They do have good Customer support as well. Once you order the TS connection via Amazon providing the installation Address, you will get a call from the TS Area/local Dealer to confirm the installation address / details. If you have any queries related to the connection, you may clarify with them. They will send the TS technician to the mentioned address for installation.
Yes, you will get the HDMI cable with the new connection which is included along with TS HD accessories / package.
I don't recommend Paytm as I have stopped buying any products through them due to their worst Customer support and product delivery delay (delay might depend on seller / courier and this may not be applicable for TS connection)