What is CURL equivalent for GenieACS "SUMMON" button?

From the API:

curl -i 'http://localhost:7557/devices/202BC1-BM632w-0000000/tasks?connection_request' \
-X POST \
--data '{"name": "refreshObject", "objectName": ""}'

Answer to your second question available here:

curl -i 'http://localhost:7557/devices/00236a-SR552n-SR552NA084%252D0003269/tasks?timeout=3000&connection_request' \
-X POST \
--data '{"name": "refreshObject", "objectName": "InternetGatewayDevice.WANDevice.1.WANConnectionDevice"}'

~ R