Do apps get shared between iPad and iPhone?

Many apps can be redownloaded to the iPad and shared, but you have to keep in mind the differences in display size. Some cases show a 2x button which you can tap and fill the iPad screen. That does result in pixelation with certain apps.

Check each app and make sure it can be downloaded a second time and that it is compatible with the iPad.

You do not have to purchase the apps again. Assuming that they are compatible with iPad, you can transfer purchases when you sync the iPad with the itunes library. You can also restore from a back up in order to transfer any app data to the iPad from your iPhone. Once again, you do this when you sync your iPad to iTunes. You should be familiar with the process since you have an iPhone already.

When viewing apps in the app store, if they have the + sign next to them, they will work on both devices.

You can use iPod/iPhone apps on the iPad and you don't have to re-purchase them (if you havn't still got copies of them on your computer then you can re-download them for free : http://support.apple.com/kb/HT2519). You can chose which apps you want to install on the iPad. By default their settings/stats won't get copied onto the iPad - it's possible that you may be able 'restore' the iPad with the iPhones backup in order to get all of your iPhone's apps/settings/stats onto it (I've never tried this so I'm not sure that it's possible). You may also need to check that you've got the relevant iOS version on your iPad for the app(s).

As a slight aside, unless the apps are 'universal' (indicated by a plus symbol against them in the app store) then they won't be coded to make full use of the iPad's larger screen - by default they will just take up an iPod/iPhone sized portion of the screen, though you can press a '2x' button on the screen so as to double the dimensions (which basically just double's each pixel in both directions so it may then appear pixelated). Universal apps have code in them to detect the type of device that they are on, and can therefore make use of the iPad's larger screen.

Michael ... when you launch iTunes on your computer, and you look in the library on the left side, there is a tab for apps. If you click on that, it will show you all of the apps in your library and it should tell you which ones are iPhone, iPad, iPod etc. Try looking at the list in the different views at the top of the iTunes screen on the right side. A couple of the views work better for this purpose than the "list" view itself.

When you are in the app store, the apps with a + sign next to them are compatible with the iPhone and the iPad.

Any app that you have already paid for can be downloaded again at no charge. Media such as movies, songs, etc would have to be purchased again.