The Office UK questions

They said in the special that David Brent successfully sued Wernham
Hogg. I can't imagine how he could sue the company and win. He was
fired for good cause and got a redundancy package.

Is "redundancy" just the British nice euphemism for firing somebody??

vague disclaimer...

Redundancy is when there is no job for you to do - there are rules for
governing how redundancy is handled, usually kicking in after mergers.
Unless you sign a Compromise Agreement (which requires you to get legal
advice), you are still at liberty to sue for unfair dismissal either on
grounds of fairness (say, someone else should have gone) or process (you
did not adequately consult).

Stephen Merchant's dad appears in some scenes as a custodial guy who
stares at the camera. I've worked with people like that.

At the end of the first season, they told David he could move up in the
company and his staff would be removed or he could stay. Why would
that happen?

vague disclaimer...

All part of office politics I suspect, putting him under pressure. It
may be hopelessly warped, but Brent has a strong sense of morals and
could be goaded into resigning on principle (kissing goodbye to any
package). I know someone who resigned a week before a merger and lost 10
years worth of severance pay.

Mostly I suspect it was for the dramatic purposes of making him choose
'his' team though.