"If my champion moves once only then passes the turn over would this exhaust my champion or would I be able to use my swift later?" - Steveo
Yes, they are exhausted. However, being exhausted does not stop you from playing swifts. The only abilities you cannot play when exhausted are abilities that have the cost, "Exhaust".
Example, if you are Malik and you move once then end your turn you are now exhausted and cannot use his Basic Attack  ability. However, if you have a cross punch in hand, you can still play it because the cost is Energy 2 and does not cost Exhaust.