Well, the large supply of vias sure stands out to me.
The lack of any connection between connector housings and top side ground also looks rather suspicious, but maybe that's more of a noise problem than a gain or oscillation problem.
Emitter bias: it's fine, as long as you have enough bypass caps and vias to keep the ground return length sufficiently short.
Otherwise, you end up with a significant amount of reactance there, which is degenerating the transistor. Or often, making it oscillate!
If you can't make the emitter stub length short enough, then you have no choice but to ground it to plane, directly (red dots in marked-up picture above), and use a collector resistor for bias feedback (as discussed earlier).
BTW, regarding port impedances: when 1/s12 << s21, the amplifier has high isolation, and the port impedances are very nearly s11 and s22, respectively. When s12 is relatively large (which is often the case in common emitter amps and such), the feedback is significant, and this affects the port impedances as well as the stability. A wideband amp with low dB's gain shouldn't have too much problem, but this is significant in tuned (narrow band) amplifiers, where you're trying to push as much gain as possible (indeed, you may then be trying to push the maximum stable gain, another parameter to be aware of!).
I would hope RFSim is taking this into account, so you should be fine there. Just to add this as FYI!
Note that inductors on the order of 7nH are just a few mm of thin trace, where "thin" is Zo some ratio above the system impedance (i.e., a reasonable inductor is a length of 100 to 150 ohm trace, in a 50 ohm system). When specified in these terms -- as transmission line lengths -- you should get even more accurate answers from RFSim. Hence why you might want to scrape at some traces, or beef them up as the case might be.
Indeed, you can express the emitter impedance, and everything else, that way: as transmission lines. I don't know if you can include all those components around the transistor, in RFSim, to create a model that is well representative of the physical circuit, but if you can, it should provide more insight into how your circuit differs from expectations.
Tim