Can I read a book I purchased on Amazon on my kindle app?

Amazon physical books and ebooks are separate. If you bought the physical book then you do not have the Kindle ebook.

In order to use a Kindle app with Amazon Kindle books you need

1. an Amazon account w/ a credit or debit card in it (can be a parent's card, and card is required to be IN the account even to buy free ebooks, and even if your account has a gift card balance)

2. A Kindle or Kindle reader app/software registered to that Amazon account.

Now you can buy ebooks at Amazon and choose any of the Kindle apps or devices registered to your account as the destination for the ebook (or use their Manage Your Content & Devices page to send the book to your registered Kindle reader).

You can also use Overdrive.com to borrow ebooks if your local library supports Overdrive. They have their own apps (PC/Android/iOS) or can loan Kindle ebooks (I believe borrowing Kindle ebooks requires an Amazon account). You can search on the right below the banner of their front page for your zip code to see if a local library supports Overdrive. They may or may not offer the ebook you need for borrowing, and if others are waiting for it then you have to queue for it and wait your turn.

Only if you buy the ebook edition. A paper book you buy does not flip to an ebook.

Or it's available as a free ebook. And that's doubtful if they are still selling as a regular book.

Yes, you can. However, you will likely not to get it free. Go to amazon.com and look on the left side of the home page, see "All" drop down menue, select "Kindle Store" and look for your book from there.

Only if you bought the ebook. Have you tried the library? They have ebooks too and you can check their inventory online from home as well.