Which of the security services can be provided by digital signature?
Yes. Digital signature can provide data / message integrity. Generally digital signatures include a hashing algorithm. The verification includes proof that the correct hash over the data was signed by the sender.
The cryptographic message syntax or XML digsig are examples.
Yes, it can. And non-repudiation also more or less implies data integrity. Because to make sure that an entity cannot deny signing the data, you need to know which exact data was being signed in the first place.
X509 certificates usually have a non-repudiation bit to indicate that the private key can be used to generate signatures for non-repudiation. Look at XAdES for an example (government regulated non-repudiation).
Yes, most certainly. The sender can be authenticated by signing a challenge in a transport protocol, for instance.
Think of smart card logins onto web sites for an example, using client side authentication within the TLS protocol.
No. Generally the receiver in a protocol is holding a trusted public key of the sender. You need to have access to the private key to be able to authenticate. If we assume that the receiver - i.e. the receiver of signed messages - only has access to the public key he can only authenticate the sender.
Obviously receivers can also assume the role of sender in most protocols, in which case the entity also holds his own private key.
As only data integrity is mentioned, you could mention data authentication. Signatures do not just provide data integrity but also authenticity, i.e. proof that the message originated (or at least was signed by) the entity controlling the private key.
That's a slightly different notion than data integrity, which doesn't provide this proof necessarily. Both properties are however achieved by a single signature.