After ACL repair, will I be able to climb stairs normally, jump, run or dance again?

Yes. Results of acl surgery are generally good but are influenced by overall condition of knee. Associated cartilage damage or unsalvageable (unrepairable) meniscal tearing do definitely adversely affect outcome. In the patient with an isolated acl tear without associated damage 90 some % will return to an active lifestyle.
Acl. The goal of acl reconstruction (we rarely if ever repair acls) is to allow the athlete and patient to return to all sporting activity.