Here are the official ports: TCP and UDP ports used by Apple software products - Apple Support
Looking at open ports tells you nothing about what is actually running on those ports.
It’s not unheard of for a malicious app to spoof another legitimate (but transient) app.
macOS uses the following range for ephemeral ports:
net.inet.ip.portrange.first: 49152
net.inet.ip.portrange.last: 65535
That iOS follows that same range would not surprise. Though technically, 1025 to 65535 was RFC-permissible as an ephemeral range, when last I checked.
Which means you’re probably looking at some local app with a TCP port open. Which would be commonplace.
TCP 62078 was usually UPnP, when last I checked. Wouldn’t surprise that iTunes sync was associated with UPnP.
There are VNC/RDP apps around for iPhone.
nmap won’t tell you much about that activity, and getting the routing information (for an iPhone, which doesn’t expose routing info) usually involves the information available on an intermediate router, such as a firewall router. That’ll tell you connection source IP and port, and destination IP and port, when a connection is established.
When a port is open and otherwise inactive with no open connections, fingerprinting is sometimes possible, but not particularly reliable.
It used to be possible to poke at the ARP tables on an iPhone, but that was discouraged. There’s source code around, if you have an inclination to test whether the ARP data is still available to non-app-store apps. Accessing other apps isn’t an option.
Open ports discussions aside, what steps have you taken to improve your security, particularly given your concerns around having been hacked? In particular, a response would usually involve a factory reset and all-password change, among other steps..
As for your own security, are you worth most of a million dollars plus another chunk of a million dollars to hack? If so, a better source of info than what can be obtained here in the communities from folks like me is probably warranted. If not, you’re not likely breached.