I Love and appreciate Khanacademy too. I will be interested in the response to this question. I was about making use of the API when I saw the sad news.

We were using the API to allow for a user to search the resources to then link to them in their LMS. Is there another approach we should be doing to accomplish this?

As a homeschooling parent who uses KH for all four of my children, this is a total bummer. I need to keep accurate records of my students (children's) learning activities. the Parent and Teacher dashboard don't do that for me. I created an app that uses KH API to automate the creation of reports and format them to my specifications using my student KH data. 

How can I get the data now? Please, respond. Thank you.

What are the plans going forward to allow for development on the Khan Academy platform? New API?

Hi, I'm also really disappointed by this :(
Was just looking into creating a learning app for myself and integrating Khan.

Could anyone from the team elaborate a bit about why all endpoints are being removed, and if there are plans on replacing them with a new API in the future?

This is really disappointing indeed.
I'd also be interested if there is another API under development or if there is a reason for the "walled garden" approach that some other commercial companies are taking. I would have thought KhanAcademy would have been the last bastion of democratized learning out there.

Are there plans for newer revision of such APIs, so KA content can be accessed by other systems?

I have a question: A friend told me I could find my user id number somehow using this API thing. How would I do that?

Love Khan Academy.  Definitely want to add my voice to the chorus of disappointed folks who had plans to leverage KA's API to maximize the benefit of our learners on this platform.