I’ll break it down:
Chinese characters seem very complex to write.
Indeed, the Chinese characters are generally complicated, for example, some characters require over 40 stokes (龘). Fortunately, such characters are not that many. Further, the stroke order is unique for specific characters. The order can be applied to the new characters as well.
Can Chinese students who hand write essays or exams write quickly?
Yes, the native Chinese can write quickly. Very quickly. They learn to write characters from childhood, and by the time they graduate from high school, they are just professional at writing Chinese characters, that too in a perfect stroke order.
What do they do if they want to use a word but don’t know the character for it?
Such scenarios are possible, but not that likely. The natives know about 5,000 characters, maybe more. That’s more than enough for daily life, or even for the business communication. However, some characters with technical meanings (i.e. medical terms) may not be known to many. In such cases, there are a variety of ways, such as dictionaries (字典/词典) and online tools, to find the characters quickly. Once the natives see a character, even if it is a rare character, they can write is quickly.
Remember: The natives don’t memorize writing each and individual character separately. Rather, they follow the stroke order to write characters. The stroke order is mastered during the early education.