You need to have enabled API documentation in your settings.json file for using API calls.

Here is the line: "apiDocumentationEnabled": true

List of mostly used API calls:

Your Qortal Node API Documentation/Access: http://localhost:12391/api-documentation/

Your core block chain height, core status (minting or syncing), number of connected nodes: http://localhost:12391/admin/status

Your Qortal Node Admin Information (your up time & Build Version): http://localhost:12391/admin/info

Your Qortal Node Information (Address, PublicKey, Blocks Minted): http://localhost:12391/addresses/(INPUT_YOUR_ADDRESS)

Adding new peer to your DB: http://localhost:12391/api-documentation/#/Peers/addPeer

If your core is stuck at some height, you can try to ditch blocks to some height and re-sync from there. You are inputting height to ditch to. If you will input 300000, your core will drop blocks up to 300000 and then start to sync from that: http://localhost:12391/api-documentation/#/Admin/orphan