Yes - the voltage divider current should be much higher than the base current. A factor of 10 is usually sufficient. Also for the Vce assumption, as others mentioned we need to ensure that the BJT never saturates through the full output swing. Another assumption is that Ic is twice that of the load current. You can have this higher but it will increase power dissipation. So a factor of 1.5 to 2 is chosen - for line-level or low power twice and for power amp (driving a speaker) a factor of 1.5 is chosen.
All said this self-biased scheme is not that great for low distortion applications. There is another factor that contributes to distortion - the BJT's internal emitter resistance which is a function of the emitter or collector current. So unless the external Re is made very large compared to it it will introduce significant distortion (this means low gain). This can be remedied by replacing Rc with a CCS but now we end up with such a large gain that Re is not sufficient - global feedback is needed.
There is also no "feedback" as such - the external Re merely introduces "emitter degeneration" which stabilises the ckt. Any feedback that is there is an effect of this. Fot true feedback we need a few distinct stages - an input stage and error amplifier, a gain stage, an output stage and a feedback network which feeds a part of the output back into the input and error amplifier stage.