The fundamental difference between hole and electron mobility is still there, and a few in-silicon processes are different, too. So you still don't get identical transistors just by flipping N and P.
That being said the common emitter circuit will behave similar for transistors with similar key specs (fT, miller capacitance, beta), independent of NPN or PNP. Of course, finding RF PNPs tends to be not as easy as coming up with a NPN.
This is because gm is purely a function of Ic, see page 24 of this class handout
Correct. Although, as you mention, too, it is only true for low frequencies, where the Miller effect may be neglected. However, the equation Rbe = Ut / Ic is still a very important one in many fields, e.g. linear supply design, AF amplifiers etc. and often disregarded (with corresponding, i.e. bad, results).