Quote: " I would like to be able to call a database from an AppGameKit app"
Unfortunately AppGameKit doesn't have any database functionality. You can still use an online database by working with the HTTP commands.
Login...Everyone expects to wait a couple of seconds to login. And you certainly never put all of the users into memory, it's a huge security flaw. If you are anticipating lots of users, then I assume it is online? You would send teh user name and (encrypted) password to the server via HTTP. This would call a program (e.g a PHP program). The PHP program does the database lookup and validates the password, sending back a true or false response to to your program. The end user never directly accesses the database.
Quote: "what response time can I expect from a large database, with say, 10.000.000 items?"
It all depends on how well you design the database
I could return a record quicker than you can look up from the keyboard to the screen...in the right circumstances. On the other hand if you are running a search for a complex set of criteria with multiple valid records, it may take a few seconds.
It certainly sounds like you should be doing this as an online database and returning only relevant information. You'll need to be keeping the data up to date, and you don't want to be distributing 2GB+ of data to numerous copies of the same repository, and keeping them synchronised. Users won't thank you for consuming gigabytes of their disk with potentially unused data. (Nobody could consume this amount of data in a lifetime unless you are performing aggregations etc on the full data).
It's all about smoke and mirrors. When you're watching an intro sequence to a game, it's not for the intro sequence. It's so the game can be loaded whilst distracting you. When you pick an option and the screen smoothly scrolls to one side, it's to fool you into thinking it's loading the next screen faster than it actually is. If it takes 2 seconds to load data, you need a 2.5 second animation to hide it, where the data appears in the last 0.5 seconds.
Take a look at some of the games you own again, you'll soon spot the smoke and mirrors.
Quidquid latine dictum sit, altum sonatur