Would a dental retainer fix one crooked tooth?

Depends on position. If correction involves a simple tipping motion to correct the position, then a retainer can correct it. If the tooth is significantly rotated and /or tilted out of line such that it would require rotational correction and /or uprighting of the root, then braces or invisalign may be required.
depends. If the tooth is slightly out of the arch or slightly rotated and there is enough space, the retainer will work well when properly designed. See your dentist to know if this is viable.
Only if... Only if there is sufficient room. Unfortunately a crooked tooth is often just the tip of the iceberg. If there is insufficient room for correction it often means all of the otherteet( have drifted out of position. For best advice see an expert at straightening teeth, a Specialist Orthodontist, for a (usually free) Initial Examination and a discussion of treatment options.
Depends. If the tooth is crooked because there is not enough space, you may need more than a retainer. Visit a dentist for an evaluation and treatment.