Having marketplace web site and native mobile applications, I'd like my users to make payments via PayPal. This is the scenario where I'm just "API Caller" and, as I understand, I need to use Adaptive Payments. Am I right?
Then it seems (according to this) that the only mobile SDK that is suitable for my use case is "legacy" Mobile Payment Library. Unfortunately the library has quite "old-school" UI, not really matching cutting the edge UX patterns (e.g. material).
What are the possibilities for me?
If you are only an API caller you can do like other 3rd party platform do (Shopify, etc...). It's called Granting Permission: https://developer.paypal.com/docs/classic/admin/third-party/
Basically the merchant on your platform grant permission on his PayPal account which allow you to make API call through his account with your credentials.
This works if you just want to be an API caller.
If you want to take a 'fee' on the payment, you'll need to use the Adaptive Payment API (you can do Parallel Payments or Chained Payments depending on your business case).
And unfortunately as you found out, the mobile version of this API is very bad and there is no proper way to integrate it inside an app.