Will I need an implant after having a root canal?

No. No. You may need a retention post and a crown. But not an implant if you just had a rootcanal done.
Not likely. If the root canal therapy is successful and you then protect the tooth with a crown or whatever other restoration your dentist feels is appropriate, the tooth can last forever and not need a replacement. We see this all the time. However, if the rct fails, or develops periodontal problems, an implant supported tooth is usually the best replacement option. Discuss your options with your dentist.
No. Perfoming a root canal on a tooth will help heal the tooth without need to extract it. As long as the tooth is still in your mouth, no implant needed. An implant is used to restore a tooth that has been extracted.
Choose only one! A damaged nerve may be treated with only 2 options. A root canal to remove the damaged tissue or an extraction to remove the damaged tissue and the tooth housing it. If the tooth is removed, the newly created space may be restored with an implant. The best treatment option depends on the circumstances necessitating the treatment.