App compatibility with a tablet I might buy Nexus 7. But how are the apps configured with this larger screen? It's in between a regular tablet 10" and a phone 4" so how, for example, will apps like 


notational acceleration 
MyLifeOrganized


and others work with this enlarged screen?
It's up to the app. Android provides mechanisms for app authors to specify different UI layouts for the different screen sizes (roughly speaking: phones, 7in tablets, 10in tablets). This means that the app might rearrange its buttons or use larger sizes to fill a 7in screen, or it might do something more radical like switch to a two-pane layout (such as Gmail). IIRC, most apps with a two-pane layout use it only in landscape mode on 7in screens, whereas they use it in either orientation on 10in screens and always use a one-pane layout on phones.

Unlike on PC, it's usual for Android apps to be laid out using a resolution-independent unit (which Android calls display-independent pixels, or dp) instead of specifying sizes in pixels, so that regardless of display resolution, buttons are always large enough to click on. There are a few exceptions (app authors can still choose to work in pixels) but those are in the minority: mostly games, since that's how PC game authors are used to working.

Even if the app isn't specially designed to work with tablets, it'll still work. It just might look silly, with lots of empty space or oversized buttons, if the author didn't consider or test that form factor. Google Play encourages developers to include screenshots on 7in and 10in tablets, so that's the first thing to look for. If you browse using the Google Play app on your device, it'll show you the screenshots for that device's size first (i.e. it'll show the 7in screenshots if you're using a 7in tablet). Many developers also explicitly mention tablet support in the app description, such as the first app you linked to (Notational Acceleration).