Purchase history - how can I view?

You say "Media and Purchases, but the "Store" which are several different stores (and it is "Apple Store").

For items from the on-line store go to apple.com, scroll to the bottom, and click on Apple Store Account. --> https://www.apple.com/us/shop/goto/account (only the past 18 months)

For iTunes and App Stores purchases you can see receipts in your purchase history: https://support.apple.com/HT204088 Apple also emails you a receipt for any charge made to your account. "Search your email for the words “receipt from Apple.” - https://support.apple.com/HT201382

For a physical Apple Store purchase you can try contacting the store where you purchased the item and see if they still have a record of the purchase.

Viewing & Changing Orders - Shopping Help - Apple - https://www.apple.com/shop/help/viewing_changing_orders - "Once an item is shipped or picked up, Apple will create an invoice for your order. To view or print your invoice, go to your Order Listing (Opens in a new window) page and select an item to go to the order details. Then, select View Invoice at the top of your order details page to access your invoice. If you need help viewing or printing your invoice, speak with an Apple Specialist at 1‑800‑MY‑APPLE."

Apple recommends you "Keep your receipt after you buy an Apple device" --> https://support.apple.com/HT202711

Purchase History - which is what I want to see.

Click on the link to 'See your purchase history in the App Store or iTunes Store' [iOS, computer, or web] - Does not include purchases made by others under Family Sharing; those have to be checked from their accounts. --> http://support.apple.com/HT204088



I guess I don't really understand what you're asking about -- you post about various things in different parts of your post.

The link I provided tells you how to see your media purchase history on various devices including a Mac.

I think this might be to what you are referring in your first section:

The resolution to this issue is often making sure you have entered a credit card or other valid method of payment* even if you don't plan on needing to use it. The document 'If you can't remove your last payment method or use no payment method with your Apple ID' mentions "if you're using an existing Apple ID with the App Store for the first time, you must provide payment information," in this link: https://support.apple.com/HT203905

If there is an option to select "Review" or "Continue", select that and enter valid payment information if required. If there's problems doing this:

Tap: Settings > [your name at the top] > Media & Purchases > View Account > Review Apple ID.

More things to try in this 2018 post by Urquhart1244 marked Apple Recommended:

https://discussions.apple.com/thread/8434425?answerId=33542414022#33542414022

If you continue to have problems contact Official Apple Support - Select your region from the list and then your country from the pop-up window. If you do not see your country, see if there is an "other" listing for that region.

https://getsupport.apple.com/?caller=cups&PGF=PGF63005

*Payment methods that you can use with your Apple ID - https://support.apple.com/HT202631

If you mean the Apple online store at Apple.com, go to apple.com, scroll to the bottom of the page, and under Apple Store, click Order Status. Only purchases from the last 18 months will be shown there.