Normally, in today's world developers test web APIs using Postman (or something similar).
https://www.getpostman.com/
FWIW, I work with web APIs every day and have not used curl in many years for testing an API. The dev world has moved on to very good tools for this in the last few years. I recommend you download, learn and usePostMan , or a free browser extension, to test API end points. It's a very good web API testing tool used by over 6 million web developers, including your truly.
Frankly, I have tried and used these tools, and in my experience using PostMan will have you a lot of development time.
The PostMan web site has the answers to all your questions except the last one. Please read the basics there, Thanks.
Regarding curl, someone who uses curl can help you. Frankly, I stopped using curl for testing or web APIs or downloading web data a decade ago.
I occasionally use curl and wget to download a file.
As a cybersecurity person, I note (as a side note) that a lot of malware uses curl when the hacker attempts to exploit a vulnerability on a web site and download malware to the file system.
You can read PostMan's documentation about their policies, but I think you can use it for free based on their conditions.
Sorry, I don't use SOAP UI, because I use PostMan and it has worked fine for me when testing an API, but that's to you to choose what you like. Download both and see which one works best for you.
I'm going to download and check out SOAP UI someday. It also looks good.