The name of the program is "The Apprentice" but during the final interviews Sugar said he preferred a lady in her thirties with more than 10 years experience to a younger man with only one year in business. Surely an apprentice is defined as a young person who joins a company to learn a trade or learn the business.
Of course "LOrd Sugar" can tweak it any way he wishes but he ought to change the name of the program if he is picking older experienced candidates.

He doesn't have an actual job for the winner, they will "slot" into whichever business he feels most suitable, so it's better to call it something general, rather than tailored to one company...I guess!

A. Because it's the UK version of the American programme / franchise of the same name.

B. In addition, calling it "The Job For A New Employee In Their 30s" wouldn't sell the programme quite so well, would it?

There doesn't have to be such a long name.
I still maintain that an apprentice is supposed to be a trainee type job not for candidates with many years of experience.

Why does he fire people all the way through....and then "hire" somone at the end? How can you fire someone you havnt hired yet?

They're 'fired' from the competition.

That's what it is, a trainee type job, in the line of work that Lord Sugar offers. What they did previously (unless it's the same line of work) doesn't really matter; neither does their age.

If after 30+ years of work in finance I decided to join an electricity company as an electrician, and they took me on, I would probably be an apprentice. But of course, in the context of the programme, the word is used loosely to mean 'learning the (Lord Sugar) trade'.