Is there a way to search, for instance "Races I dont own" and it could show me what races/feats/whatever and I could click to buy all right there or do I have to go book by book to check?

As far as I know there is no one stop click to buy parts of books other than one of the bundles that will buy all books, source books or adventure books. These are to buy the complete book not just the parts you want, and you get credit for anything you have already purchased.

You can use the Races, and Feats under the sources tab and they are grouped by book; feats can be sorted to some extent. If you click on a race/feat you do not own it will take you to a paywall to purchase the book or parts of it.

Or go to the legendary bundle purchase page and see all of the books you don't own and start adding them to your cart the books you own are greyed, books you don't are black.

Check your purchase history through the market place tab, or through your account it has a marketplace tab as well.

Also if something is shared with you you wont get the paywall to buy it.