Access multiple non-standard ports on the server through a single VIP - can you do it, and how?

The safest way is to create multiple Virtual Servers, all for the same IP address, each with different ports, and with different pools pointing at the appropriate server-side port on the pool member. It's easy, fast and it works.

> From the client side, is it simply accessed in a browser using 'mysubdomain.mydomain.com:65001'?

Yes.

> Would the 'https://' or 'http://' prefix be needed?

The http:// prefix tells the browser to use the default http port (80) without TLS encryption.

The https:// prefix tells the browser to use the default https port (443) with TLS encryption.

If you override the port in the URI, then https:// or http:// specifies whether TLS encryption is used by the browser or not.

So using TLS depends on either the virtual server (client-ssl profile or not) or the pool member service listening on the target port (if the virtual server is a passthrough).

You should not need any irules or LTM Policy.

If you use an :any virtual server (all ports) you need another mechanism for control (maybe to block port 22 for sshd, and port 23 for telnet, and ...). You also need complex mechanisms (like irules or LTM policy) to allow for server-side port translation, pool selection, client-side and server-side SSL profiles. It can be done, but there are generally better solutions.