A full train station is filled to capacity. A teeming train station is beyond full—it’s abounding or swarming with people. Teeming comes from the verb teem meaning “to abound or swarm,” or “to be prolific or fertile.” The earliest sense of the verb was “to produce offspring.” Given the fertile history of this word, it is not surprising that teem often appears in close proximity to the word life, as in the case of a tide pool that is teeming with life.
Relationship is a general term that can be applied to a wide range of connections, involvements, or associations—each of us has a particular relationship with technology, for instance (some better than others!). The noun rapport is more specific: this term is used of relations between people and suggests a harmonious and sympathetic type of connection. For example, a teacher might try to establish a close rapport with students—a connection marked by mutual understanding and good communication.
Something that is fortuitous happens by chance or without known cause. In modern standard use, the term almost always carries the senses both of accident or chance and luck or fortune, as in the case of a fortuitous encounter with a former acquaintance that leads to a promising new career opportunity (a happy accident!). Beware that some stylists and editors may object to the use of fortuitous to mean anything more than "accidental." In formal writing, when your intended meaning is less about a happy accident and more about fortune's favor, the adjective fortunate may be a better option.