To get the answered and not answered records sum instead of count. To get the number of all records that are either answered or not answered use count(status). To get the count of all records, i.e. also records with status null use count(*). Strings need single quotes, not double quotes. The case statement needs END.
EDITED (there were too many END used):
select call_type, channel
, sum(case when status='no answer' then 1 else 0 end) as cnt_no_answer
, sum(case when status='answered' then 1 else 0 end) as cnt_answer
, count(status) as cnt_all_stated
, count(*) as cnt_all_records
from app_account.cc_call
group by call_type, channel;