Whether any external agency can provide eSign service?
As of now, only CAs are allowed to operate as eSign Service Providers. However an external agency can become ASP of ESP.
Whether ASP is allowed to sublet the service to any other application owner?
No. ASP can avail service from ESP for integrating eSign service only for applications owned or operated by them. The functions of obtaining consent from the signer and its logs should be with ASP only.