Unlike a default, which can be indicative of as little as a missed payment, the CCJ generally occurs because you have constantly missed payments, and very often failed to engage in any form of negotiation with the lender in question. The CCJ is issued by the court and represents a legal instruction to make payment within the timeframe specified by the court. If you are having debt problems, try to avoid the CCJ at all costs and negotiate with the lender as early as possible.
Most lenders really do want to help, and regard court action as an absolute last resort.
Under certain circumstances, yes. However you will need to apply to the Court to have the case reopened on the grounds that you did not receive 'due process' first time round, ie you didn't get the summons. Then you have to go back to Court, and when the judgement is made again, pay it off within the 28 days. That's the principle, the practice is more complex. Seek legal advice.