Normally applications are in their own folder, called Applications and as such are available to all users (user accounts). If they are in that location you will not lose those applications, but you will lose any data that is within the Home folder you wish to delete.
Check that home folder ("my original admin account,") contents in Finder before you delete that account from the Accounts panel in system preferences.
Often data such as emails are stored in the Library within the user's folder.
Make sure you have another fully functioning admin account before you delete it.
It is usually better to use another account for some long time before deleting an account so that you can see what the limitations are and, if necessary, transfer items from the original account.
Having a bootable backup of the whole Mac on a external disk is very useful and something I advise everybody to have.