Your mother's iPad will take you through the process of creating an Apple ID, but you can also create one on her behalf at Apple's website. Whatever you specify as the country of her mailing address there will determine the Apple Store she becomes associated with.
So the answer to your first question is yes, it is based on the Country/Region you specify when creating a new Apple ID.
The answer to your second question is no, it doesn't matter what you set as the regional localization of your iPad itself. You can change the iPad's localization as often as you like, indeed I do this when moving between the UK and the US. The iPad localization determines things like date and telephone number formatting conventions, spelling dictionaries, and so on.
As an addendum, you can have multiple Apple ID's on a single device. This is kind of annoying to do, but sometimes it's the only way to get an app. In my case, my main Apple ID is linked to the American store, but my London bicycling maps are only available on the British store. So I maintain two different Apple IDs, and when I update my apps I have to type in both passwords and juggle them a bit.
Your mother may not want the hassle of doing that, in which case you are well-advised by @stuffe to keep everything on a single ID.
First make sure that ALL the apps are downloaded/purchased from your account. If not, only your apps will update.
If you want to change account go to settings->iTunes & App Store->Apple ID->Sign out->and enter your other account.
Best Answer
Go to Settings → General → Restrictions and set Require Password to Immediately to always be required to enter your password for purchases.