Climbing on tribike vs regular road bike

Ya.  Skip underwear.

I find it hard to be out of the saddle with decent balance on a tri bike.  I try to keep my out of the saddle times to a min to save the legs.

Not sure about in the saddle differences.

Yes, you got it right.  The climbing power difference between road and tri IS from position (geometry)and from the different muscles you use. 

Didn't the person doing the professional Fit notice you were wearing underwear and try and correct you?  Shame on them.  

Reading into your questions, are you asking about which bike to use for group rides, training, or on tris?  For me personally, my cycling rides and training are for tris and not for other cycling events so i try to maximize the time I use my tri bike, esp. for and long distances and even on hilly rides.  This year, I've used my tri bike on all my long training rides this year, 4 centuries, and the AIDS ride (545+ miles).  Granted, it was not the optimal bike in some cases for the fastest ride (esp. on the hills.  Plus, I have to admit I was also overgeared for one nasty stretch with a Cat 1 climb), but it was optimal for my tri training.

only chamois butter under the bike shorts for me...definitely no underwear or other clothing.