I am assuming you are using all of the defaults. So what does your host file look like? I normally use ansible on the networking side - so it is little different then servers so take everything i am about to say with a grain of salt. I don’t have a server to test these commands against - this is just how I would start to approach it.
I would think that you would want use gather facts to find out what server type you are hitting or assign the variable in your host file. Your vars prompt is not needed, you should have that information in your host file. When you run your playbook it will use the username that you are logged in as on the control node. If you want to change that you would use the -u in the command when you execut the playbook. Also the password you would use a -k in the command.