Cronjob for 1st of January every year

Yes, that looks like the very new year midnight.

Yes that is correct.

Here is a quick chart you can use for future reference

# *    *    *    *    *  command to execute
# ┬    ┬    ┬    ┬    ┬
# │    │    │    │    │
# │    │    │    │    │
# │    │    │    │    └───── day of week (0 - 6) (0 to 6 are Sunday to Saturday)
# │    │    │    └────────── month (1 - 12)
# │    │    └─────────────── day of month (1 - 31)
# │    └──────────────────── hour (0 - 23)
# └───────────────────────── min (0 - 59)

Yes, and you can also use @yearly or @annually which are synonyms for 0 0 1 1 *.

(This applies at least to many distributions, but check yours to be sure.)

See also: man 5 crontab and http://en.wikipedia.org/wiki/Cron