UML Sequence Diagram – How to Show an If Statement

They seem to be correct enough to understand what is going on, which in my opinion is all you need for UML. However if you want to be more technically correct:

• Request membership card appears to be a return when it should presumably be a message with provide membership card as a return?
• confirm membership may not need to go back to the person, but a request for the book name probably should

I would say go as high level as you can while still including all the necessary method calls, etc for your topic. My reasoning for this is that if you're including every single interaction then you might as well just write the code yourself.

Personally, I have always viewed sequence diagrams more or less as "guidance" for the implementer. I've never viewed them as living documents - if the implementation differs from the design I won't go update the diagram (unless it's different because my design was wrong). However, you're right in assuming that it largely depends on the audience.

If you have a team full of experienced developers with knowledge of your product, you should be able to leave a few things out here and there and trust them to fill in the blanks with their best judgement. In my case, I usually confine my sequence diagrams to a particular topic, say "Process XYZ", and only show method calls and object interactions that are relevant to that topic, leaving out things in between that are obvious or are defined in another diagram. If I'm writing a diagram for a junior developer who's learning the project and domain, then I tend to be more specific.

The only reason I would include every single method call and interaction is if you're actually generating the code from the model. For example, I've worked on some embedded systems where we generate our code out of a Rhapsody model, so obviously in that case you should include as much as you can.