If I get a second iPad will I have access to all my apps? Do I need to purchase them separately for every iPad I have?
As long as you log in on both iOS devices with your same login from Apple (or backup and install them with the same login on your Mac/PC with iTunes), you will be able to use the same apps and other data without the need to purchase them again.

You can still manage your apps separately for each device: For instance, iTunes will keep them apart (you get to name each device yourself), and you can install different sets of apps and photos, music and all on the devices. But anything that comes from the App Store is linked to your Apple ID login - and once you've purchase something with your ID, you can install it on all your devices.