There's a few questions here and I can't say I'm particularly familiar with the Acer One system, but first we need to clear a few things up.
First, in Linux, the administrator is known as "root". But depending on how Acer has set up your system, it maybe, that you are indeed required to be the administrator. The problem is, instead of just using one of the many terrific Linux distros available, these manufacturers will "fiddle" with the system and hence the whole thing becomes non-standard.
Second, when you say you are trying to download Flash Player, I wonder exactly what you mean. Normally in Linux, there is a distro "repository" that has all the software you need for your computer, already configured and ready to go. All you do, is mark an application for installation and the system downloads the app. and installs it for you without any further input from you.
Third, if you're trying to download a Windows exe file, there is no way it will work in Linux, so don't even try.
You may be well advised to look at the Acer One forums, as almost certainly, someone has done what you wish to do before you and all the information will probably be there for you to see.