Chosen Solution

Hi, I tried to replace my iPhone 5s battery but now the Touch ID is not working and I am also not being able to charge the phone. While trying to remove the battery I think I damaged the cable support bracket:

Can this possibly be the reason for these two problems?

The home button connector on the charging port assembly is damaged. You will need to replace the charging port assembly which should also fix your charging issue at the same time. Here is a guide and where you can get the part in case you want to buy a replacement part from iFixit: iPhone 5s Lightning Connector Replacement iPhone 5s Lightning Connector and Headphone Jack

Looks like you have damage one of the pins. Unfortunately i cant advise you repair until you wount upload clear picture of connection it self including female one (buttons)