Can I buy a iPad Pro on amazon and buy the applecare afterward?

You can buy it directly from Amazon at the same time that you buy the iPad. If it is not offered by Amazon, be very careful to understand what it is that you are buying. Amazon also sells "renewed" products and you will not be able to buy AppleCare for them through Amazon or Apple. See the screenshot below for AppleCare+ from Amazon on a new iPadPro 11.

If it is a new product sold by Amazon you can buy AppleCare+ directly from them or you can buy it within 60 days from Apple. See information in AppleCare Products - iPad - Apple

It is 60 days from purchase date. See the following from AppleCare Products - iPad - Apple

How to buy

1. Purchase AppleCare+ with your new iPad.
2. Or buy it within 60 days of your iPad purchase:

• • On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)
  • Online (requires you to verify your serial number and run a remote diagnostic)
  • At an Apple Store (inspection of iPad and proof of purchase are required)
  • By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

Yes. See the information in AppleCare Products - iPad - Apple

including

Every iPad comes with one year of hardware repair coverage through its limited warranty and up to 90 days of complimentary technical support. AppleCare+ extends your iPad, Apple Pencil, and Apple‑branded iPad keyboard coverage and includes up to two incidents of accidental damage protection every 12 months. Each incident is subject to a service fee of $49 for iPad and $29 for Apple Pencil or Apple‑branded iPad keyboard, plus applicable tax.1 In addition, you’ll get 24/7 priority access to Apple experts by chat or phone.2

and footnote 1 in the same article:

1. Service coverage is available only for iPad, its original included accessories, one compatible Apple Pencil, and one compatible Apple‑branded iPad keyboard used with your iPad for protection against (i) defects in materials or workmanship, (ii) batteries that retain less than 80 percent of their original capacity, and (iii) up to two incidents of accidental damage from handling of your iPad, Apple Pencil, and Apple‑branded iPad keyboard every 12 months, each incident being subject to a service fee of $49 for iPad and $29 for Apple Pencil or Apple‑branded iPad keyboard, plus applicable tax. Any unused accidental damage incidents will expire and you will get two more accidental damage incidents to use within the next 12 months of continued coverage. Replacement equipment that Apple provides as part of the repair or replacement service may be new or equivalent to new in both performance and reliability. AppleCare+ coverage begins on your AppleCare+ purchase date. See terms for full details.

That depends on the iPad model - I just paid $129 for an 11” iPad Pro. And yes, you have 60 days to buy it after you purchase your device.

https://www.apple.com/support/products/ipad/