what is the rest api details to load the entire configuration from a bigip device

You can generate a UCS file and download.

Generate

curl -sku admin: https:///mgmt/tm/sys/ucs \
  -X POST -H "Content-Type: application/json" \
  -d '{"command":"save", "name":"/shared/images/sat.ucs"}'

By default, ucs files are saved under

/var/local/ucs

. Here,

/shared/images

is specified because it is the location where you can download files via iControl REST.

Get the size of the file

curl -sku admin: https:///mgmt/tm/util/unix-ls \
  -X POST -H "Content-Type: application/json" \
  -d '{"command":"run", "utilCmdArgs":"-l /shared/images"}'

Download the file

curl -sku admin: https:///mgmt/cm/autodeploy/software-image-downloads/sat.ucs \
  -H "Content-Type: application/octet-stream" \
  -H "Content-Range: 0-41609/41610" -o sat.ucs

Specify the size of the file in

Content-Range

header: Start (0) - Last (size -1) / Total size.

See Demystifying iControl REST Part 5: Transferring Files for more on iControl REST file transfer methods.