ERROR "The requested profile (/#create_new#) was not found" during rest call to create a vip via iapp

The published library of iApps were designed before the REST API, and were not originally intended for this type of use, but it can be done. You're example almost works. I'm not sure that the extra escaped quotes are necessary. The following POST works for me on version 12.0:

{
  "name": "test2",
  "partition": "Common",
  "template": "f5.http",
  "tables": [
    {
      "name": "basic__snatpool_members"
    },
    {
      "name": "net__snatpool_members"
    },
    {
      "name": "optimizations__hosts"
    },
    {
      "name": "pool__hosts",
      "columnNames": [
        "name"
      ],
      "rows": [
        {
          "row": [
            "www.me.com"
          ]
        }
      ]
    },
    {
      "name": "pool__members",
      "columnNames": [
        "addr",
        "port",
        "connection_limit"
      ],
      "rows": [
        {
          "row": [
            "9.3.6.9",
            "80",
            "0"
          ]
        },
        {
          "row": [
            "9.6.3.9",
            "80",
            "0"
          ]
        }
      ]
    },
    {
      "name": "server_pools__servers"
    }
  ],
  "variables": [
    {
      "name": "asm__use_asm",
      "encrypted": "no",
      "value": "/do_not_use"
    },
    {
      "name": "client__http_compression",
      "encrypted": "no",
      "value": "/create_new"
    },
    {
      "name": "client__use_wa",
      "encrypted": "no",
      "value": "yes"
    },
    {
      "name": "monitor__monitor",
      "encrypted": "no",
      "value": "/create_new"
    },
    {
      "name": "monitor__response",
      "encrypted": "no",
      "value": "Server Up"
    },
    {
      "name": "monitor__uri",
      "encrypted": "no",
      "value": "/bigip.html"
    },
    {
      "name": "net__client_mode",
      "encrypted": "no",
      "value": "wan"
    },
    {
      "name": "net__server_mode",
      "encrypted": "no",
      "value": "lan"
    },
    {
      "name": "pool__addr",
      "encrypted": "no",
      "value": "1.8.2.9"
    },
    {
      "name": "pool__pool_to_use",
      "encrypted": "no",
      "value": "/create_new"
    },
    {
      "name": "pool__port",
      "encrypted": "no",
      "value": "80"
    },
    {
      "name": "ssl__mode",
      "encrypted": "no",
      "value": "no_ssl"
    },
    {
      "name": "ssl_encryption_questions__advanced",
      "encrypted": "no",
      "value": "no"
    },
    {
      "name": "ssl_encryption_questions__help",
      "encrypted": "no",
      "value": "hide"
    }
  ]
}