Best way to import and/or upgrade Oracle database
That is possible.
Not really needed. You can just simply transfer the database to the new server, and run the PSU postinstall script there, that takes like 1 minute.
Depends on some factors:


platform of the old and new systems
size of the database + hardware environment (network/disk transfer speed and CPU power)
downtime allowed
Standard or Enterprise edition
archivelog mode enabled
have backups
need the current state of the database on the new server, or yesterday evening is good enough
can use licensed extra products



Some other methods:


RMAN restore from backup (and run the PSU postinstall script)
RMAN duplicate from active database or backup (and run the PSU postinstall script)
RMAN transportable tablespace/database
configure Streams replication and switch to new database
configure GoldenGate replication and switch to new database
configure the new host as a Data Guard standby then perform a role transition (and run the PSU postinstall script)


There is no best method. It depends on your actual task/environment.