How does UDP track connections?

Your first para is correct. There is no connection, though some IP engines use source address/port and destination address/port to provide a synchronicity-based approximation to state.

Refusal is handled with ICMP, often ICMP port-unreachable (type 3 subtype 3).

Your last para is also correct; it's up to your application to ensure that UDP-transmitted data is correctly sequenced.

There is no connection in UDP. It is not a reliable protocol. If transmission reliability is desired, it must be implemented in the user's application. Have a look at this page.

Yes, packets may arrive out of order and may be lost. The application should take care of these things if needed.