Ok, first off I'm going to assume this is not a Part 135 charter. All this is for Part 91

1. Yes you can log all time that you are sole manipulator, as long as you have your high-perf/high-alt/complex endorsements. C421's are certified above 25000, so a High-Alt endorsement is required to log PIC

2. I would highly question any "dual-given" that you'd be doing towards this corporate pilot. Regs are gray, but honestly you don't have any time in the plane, and logging it as you being the one teaching is falsification in my eyes. In the end, only log actual dual-given as such.

3. Help out, and really learn the systems and handling characteristics of the airplane. Doing some grunt work will really make you appreciate the opportunity, and obviously so will the company that you're getting some free experience off of. 421's are good twins, but you really have to respect those geared engines. If you don't know what I'm talking about, then maybe you should sit and talk with the pilot some more.

Part 135:

Basically you can't log any of the "live" legs of a 135, unless you have recieved specific company training for that aircraft, and taken some sort of test and check-ride. All the dead legs would be acceptable, and the rules above do apply

I could rant forever, but do what you want in the end. I've known people that logged anything and everything when they were in the aircraft, regardless of the situation.