REST API for text editor keys?

I don't believe there's a REST API method for that, but you should be able to do something like that using a Studio Endpoint. If you're not familiar with endpoints already, I'd suggest starting here:

http://lithosphere.lithium.com/t5/developers-knowledge-base/Working-with-Lithium-Studio-Endpoints/ta-p/60240

Your endpoint code might look something like this:

<#assign textKey = http.request.parameters.name.get("textkey", "") />
<#if textKey?? && textKey?has_content >
     ${text.format(textKey)}
</#if>

To get the text string value, you would make a request to the endpoint and specify the text key name as the value of the "textkey" query string parameter. Please note that this is going to give you the text value in the language of the user accessing the endpoint. It sounds like you're planning on some kind of client-side approach anyway, so that may work fine for your purposes.

I hope this helps!

-Adam