Please describe your home network. I take it the Mini and MBAir are networked via a router? Wired or wireless? And what do you mean by "outside" the network? Do you wish to access the HD remotely, for example from another location?
Lots of questions, but I don't want to try to guess what you have and what you want to do.
I have DSL-router and both are connected to that. Soon I will update to Airports but I guess it doesnät make difference in this.
I have to goals in this issue. When I say "outside", I mean remote access from other location as you thought. Other thing which I need to have is the HD to work as a network HD, so I can have for example my Lightroom library pointed to that location. I have lightroom in two different computers, my desktop Win-PC and this Mac Mini.
Sorry if I describe this slightly unclearly but please ask more questions if needed.
This is not a simple issue. You can set up a network, and set up sharing on the Mini, so that other computers on the same network can read and write to the external hard drive connected to the Mini.
To do that you have to get both computers on the network first, then set up the external hard drive so others can read on and write to it.
Is that what you want to do? If yes, and yu need help with this, please post back.
If you want to store apps on the external, and run them from a networked Mac, that is a whole other issue. To do that you need to set up the Mini to be a network server:
Please post back, because I'm not sure I'm answering your questions.
In theory yes 'Back-to-my-Mac' should let you do this. You would need to turn on Filesharing on your home Mac, and have both it and your remote Mac logged in to the same iCloud account.
Thanks all. After all I am going to solve this in a proper way. I am getting a NAS or server which will work as an individual station so I don't have to do any tricks with the sharing etc.
The NeatGear ReadyNAS range include free software called ReadyNAS Remote which will let a Mac, PC, iPhone or Android remotely access the NAS server.