Does the Bible make any references to courtships (relationships between men/boys and women/girls)? What happens if I'm in a courtship and I kiss another female?
The Bible has little, if any, to say about courtship because courtship is a relatively modern concept. Throughout the time in which the Bible was being written most marriages were arranged by the parents, as we see in Genesis 24, and the couple may not have even seen each other before the wedding. In Genesis 28 we see Jacob picking his own wife, although his choices were restricted by his father, but learn nothing about their courtship.
In the New Testament, Matthew 1 indicates that engaged couples did not engage in sexual relations, because it was a potential scandal that Mary was with child. Other than this, nothing appears to be said about courtship.
What happens if you kiss someone else while engaged to a person might depend on the nature of the kiss. If it is a simple kiss of greeting as is practiced in many places that would be different than a kiss that might be shared between a husband and wife. The one would mean nothing. The other would call the sincerity of the one kissing in question. So it really depends on the type of kiss.