Is there a list of available esl-api-version?

Hello r-mikolajuk, Those are just spots in the documentation that likely need to be updated with the current version (or just remove the version altogether). Unless you're installing on-premises, eSignLive is a service that is constantly updated to the latest version. I believe the current release version is 11.0.6. If you have signed up for a sandbox recently under sandbox.esignlive.com, you would be on this version. apps.esignlive.com is also on this version. If you happen to be on sandbox.e-signlive.com or apps.e-signlive.com (notice the '-'), this is still, as of this post, on the old platform (10.13.x). The old platform will migrate to the 11.x platform at some point in the not too distant future and all will be back on the same version again. Hope this helps clear things up. You can always visit the trust center for up to date version releases and for info on outages or other issues. For release notes, you can go here. Finally, for SDK usage, eSignLive is backwards compatible, so the older SDKs (within reason) should generally work with the latest version. So, if you're using 10.13 SDK on older platform and the update to 11.x happens on that instance, there will be no issues with the older SDK. Hopefully this helps answer your question.

If I'm using just the REST API I can remove the version at all?

You do not need to include a version when calling the REST API, no.