Can I download apps via my Linux PC then install them on Android from there? I have a Motorolla Citrus smart phone.
I have Linux Mint Nadia Cinnamon

I am a total newb to smart phones and don't understand much of the terminology and what can be done.

I am temporarily out of data/an internet connection on my plan.

Is it possible for me to download an app from the google apps "store" to my Linux PC, then to transfer it over to my Android/Citrus? 

If so is there a guide that explains it in baby steps?

If not, my phone is a "3G", how fast would it take to download an app?  I could probably go to a Starbucks or somewhere with a WiFi connection.

Thanks
You can connect your device to the internet (using Wifi) and continue to use it just as you would with a plan.

So you can download as many apps as you want to your device using Wifi.

You don't need to be connected using the cellular network to access the Play Store (but do need the internet).

There are certain alternative App stores that are trustworthy, but be wary of downloading APKs directly off the internet.  There is no guarantee these are safe - generally, use the same caution you would use downloading software to your computer on your phone.  Only install from reputable sources.

You can actually pull an APK (Android App Package) off one device, and put it on another (using your Linux box), but this is not a task for a newb (you would need to install and use the developer tools)