Is part of a year always considered one full year?

In general yes, part of a year is considered a year. For example, when counting the mandatory wait of 3 years before eating the fruit of a new tree (=orla, see Vayikra 19, 23, in the 3rd year one must redeem it on a coin before eating, and from the 4th year on one can eat without redeeming), if one planted a tree in the early summer, that year is already counted, even though it was just 2 months before the New Year. Similarly in counting the years of a king, the Tanach would count someone who began his reign a day before the 1st of Nisan and died a year later on the 2nd of Nisan as if he ruled for 3 years, even though it was only 356 days. On the other hand, in business dealings, the Jewish law follows the common usage of the phrase. So if a camel (or car) rental contract states "The rental is for a year" without more detail, than the judges would have to ascertain the common practice and phrase usage in that particular place for that particular topic. In this example, today, it would be for either 354 (the regular Jewish year) or 365 days (the secular calendar year), whichever is more accepted in the locale, and when Rosh HaShana (the New Year) falls would be irrelevant.