By far the dominant system within the Roman Republic / Early Roman Empire was to simply list who were the consuls in a given year. One wouldn't say in 183 X happened. Instead you'd say X happened in the year of P. Claudius Pulcher and L. Porcius Licinus.
Towards the end of Republic using "Ab Urbe Condita" became an alternate system, counting from the supposed date of the founding of the City of Rome. People also dated according to the reigns of the Emperors. The Book of Luke for example mentions that John the Baptist started preaching in the 15th year of Tiberius' reign. Other groups within and out of the empire used their own counting systems, usually dating from an important event. Reginal systems (counting from the "crowning" of the local leader) were probably dominant. We don't know for certain as few of these groups were documenting much about their calendars.
Within the Levant (including Jerusalem) the dominant system was what is called the Seleucid Era, also called the "Era of Contracts." This commemorates Seleucus I (Nicator)'s reconquest of Babylon and the establishment of the Seleucid Empire in 312 BCE. The historian Josephus used Era of Contract dates in his works. It can be found in Syrian records until at least the 12th century CE.
To move on and answer your second question... no one knows.
The gospels weren't exactly concerned with precise dating. In fact some of the rough dates we are given are contradictory. Matthew dates Jesus' birth to 4BCE or earlier. Luke links Jesus' birth with Quirinius' census which was in 6CE.
According to Luke, John the Baptist started his ministry in the 15th year of Tiberius' rule. Depending on what he meant by that, we're talking about 27CE or more likely 29CE. John then preached for at least a year, and likely for several years before baptizing Jesus, which is generally marked as the start of Jesus' active preaching. Jesus then preached for three years (according to John) or maybe only a single year (according to Mark, Matthew, and Luke). All of the gospels are vague enough that it could have also lasted longer.
So Jesus may have been executed as early as 29CE and as late as 36CE. It's traditionally been given as 33CE. Beyond that we can't narrow it down. It has to be after 29CE because that's when Herod Antipas gets Galilee. It has to be before 36CE because that's when Pontus Pilate stepped down from the governorship.
What do you mean by the "west"? Rome? The Celtic or Germanic tribes? The Jews? Different political and cultural groups had their own reckoning of time.