Algorithms in OCSP response

Hello, I am trying to get a feel for what algorithms in the OCSP response
an OCSP service provider should be able to influence.  Can anyone inform me
if I am misunderstanding any of these statements below?

It's seems the hashing algorithm directly under Certificate ID in the
response, is dynamically chosen based on the hashing algorithm in the OCSP
request. (for example, if the request uses -sha512, the hash alg will
always be sha512)
Also, it seems like Signature Algorithm is chosen based on the Signature
algorithm of the CA who issued the cert in question*. *However, my
understanding is that this algorithm is allowed to be explicitly chosen by
the OCSP service provider, and does not have to follow the algorithm of the
issuing CA. I have pasted an modified example of a request and response
that I am trying to infer knowledge from
*. *


*Example Request:* openssl ocsp -no_nonce -CAfile trusted_cas/mycas.pem
-issuer issuser_cas/myissuer.pem -*sha512* -serial 0x02 -url
http://myresponder.com:8080 -resp_text
*Example OCSP response:*



















*OCSP Response Data:    OCSP Response Status: successful (0x0)    Response
Type: Basic OCSP Response    Version: 1 (0x0)    Responder Id: C = XX, CN =
Responder    Produced At: Jul 26 14:39:36 2016 GMT    Responses:
Certificate ID:      Hash Algorithm: sha512      Issuer Name Hash:
DDEEB63482BF2A3D64EFC2FE18AD8FD638C9E0DC8193C749619DBD0A30972573E2746B\F27047FBAAB7C6313342674FFC073739D98D82B4CF903E9755726E7579
Issuer Key Hash:
B41DE0663D1ACB30F533750F820FC9902E33B979385AB5856B9E7F6F9F7611DCB3FB759DBF\F76260CFE17CB1EF79FC31C1789F612D4F58216125ED5B445C4CC3
Serial Number: 02    Cert Status: good    This Update: Jul 26 14:39:36 2016
GMT    Next Update: Aug  5 14:39:36 2016 GMT    Signature Algorithm:
sha384WithRSAEncryption*

* <obfuscated>*




*      Response Verify OK0x02: good    This Update: Jul 26 14:39:36 2016
GMT    Next Update: Aug  5 14:39:36 2016 GMT*

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