This is why important to use with real models and not with ideal parts.
personally i suggest to use with model and not with s par.
try to reduce the value.. let say to 100pF, Xc should be around 0, so 100pF should do the job but check the other parameters...
regarding to the second question theoretically it might oscillate but please check what gain do u have at this point
i think if u working at 2.4G and it happened at 9G it not so bad, of course don't give up and try to fix it