I flew the MU2J (long) about 30 years ago or so. I did go to Flight Safety for initial training.
.One thing to remember is the difference between Vyse and Vxse. It does take time to get to single engine best rate of climb speed. but you are pretty close to single engine ANGLE of climb speed shortly after takeoff.
I operated out of a 2500 foot strip and every takeoff was a critical one. And in this case I would call for gear up as soon as we had positive rate of climb. You can't cover yourself everywhere in this plane...its not like a transport with V2 and all numbers making sense.
Do respect this plane at all times. I found it disharmonious in pitch and roll...so get use to it.
The FAA wants special attention with this plane and your friend probably bought it cheap for a reason.
The pilot who mentioned rigging is very , very RIGHT. So be sure this thing is well maintained.
Be sure to understand the fuel dippers/engine limiters/temp/torque.
Flight Safety trained us to do the ILS , both engines, with only half flap...I didn't like it that way as they encouraged us to land with half flap....but that was A LONG time ago.
My plane did not have anti skid brakes...I wish it did ! So be careful.
I had a flameout in one engine shortly after starting it on the ground...always felt it was due to an odd angle of crosswind and engine inlet. Started it again and no problems (no fuel pump problems or anything wrong).
I did have a fuel pump failure inflight...at that time the flight safety folks said to land ASAP as the pump could break apart and make alll fuel unusable....thought we landed safely.
The plexiglass windscreen can offer less than satisfactory visiblity especially at night.
I would always do stableized approaches based on weight/vref and a single engine go around at some points to a short field would be very difficult, so comit to landing at some point if an engine fails during approach.
I would say this type is one of the most demanding planes I've ever flown...true transports like the DC9 and 737 are much more enjoyable to fly.
The garrett engine is preferable to the pratt and whitney in terms of immediate response.
Rumor had it that the MU2 was going to be a pure jet at some time with no major changes except the engines.
Remember refueling is demanding and the thing can look one wing low, so fill a tip tank half way, go to the other and fill it all the way and then come back and fill the first tank up. And watch the spray as air pressure is used to move fuel from tips to main.
It will either kill you or make you a better pilot! good luck.