How external users can access the SharePoint application in case the SharePoint is connected to our company active directory.

I have created a Publishing Web application and I have specified that SharePoint is connected to our company Active Directory. Now all our employees are able to login to the SharePoint publishing site within our intranet without any problems.
But two additional questions just rose in my mind which I cannot figure out:-

1. Let say an employee login to the SharePoint website from him home using his PC ? Will he be able and how he will be able to login to the SharePoint web application?
2. Regarding external customers. I was thinking that we can create new active directory account for each external customer. But this was refused by our system administrator.
So since the SharePoint is connected to AD, so how I can allow external customer (who are not inside our active directory) to login to our SharePoint Publishing site and see cerain pages inside it?

Thanks in advance for any help.

Best Regards