There are two problems you have to manage.
First the required Andorid-version that you can find here in the app-sector on the right side of the screen. If the app needs Android 2.x you don't find it in the market.
Second: Your X 10 mini has a smaller screen-resolution. Most of the apps are not compatible with that. You can try alternative markets like the App Center
here from AndroidPIT. But I think the apps wouldn't work with your mobile.
But perhaps there are alternative apps for your apps that you are looking for. Say us, what kind of apps you want. Perhaps we can help you with alternative apps.
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Für ein friedliches Miteinander"