Honor Level 0 - End Of Season Rewards

According to the end of season rewards page, no. you won't receive honor rewards if you demoted honor, after august 1st.

And if you were banned at any point after august first, i believe (don't quote me on this) that you won't receive your end of season ranked rewards either.

End of season rewards (i assume you mean victorious skins, ward, etc.) has nothing to do with your honor level. I believe honor level is a different set of rewards.

If you are time banned after the cut off date in august (i forgot the date) and dropped your honor level, you will not get end season rewards because of time ban.

If you are chat banned at any given time and dropped your honor level, so long as you complete your chat restricted games before end of season in November, you will still receive your end season rewards even if your honor level is 0.