Can I fully control the gateway and the ESL, no internet/cloud access required?

If the 2.4G gateway provides a HTTP interface, I assume that's all I need to fully control the gateway and the electronic shelf labels , no internet/cloud access required?

Yes, if you only use it in the LAN, and the number is small, you can use our Sertag gateway as an electronic shelf labels server and you can directly call the http API of our server.