1# Questions page[archieve page] can be created automaticlly upon Anspress activation, but questions page is invisible at wordpress setting>your homepage displays> a static page>select
2# it show user not login even I am administrator and already logged in backend, but is still show not logged in at frontend.
In this case, I can comment or any other post as a logged in user, but I actually can not post or comment on Anspress question and answer.
Actually, I met this issue on your official support site several time .
3# f use Login with Ajax plugin to login, I can login and make post question and comment, but
Undo your vote will show overy time when push vote: http://prntscr.com/ippk4r
4# The number on question display 0 even after Re-count
#1 is not an issue. it is done by us to prevent admins from setting question page as static home page.
#2 Login and authentication is related to core, AnsPress is not responsible for anything related to login or authentication. Login issue happens due to caching plugin. My site had this issue few months ago due to Redis caching and that was fixed already.
#3 Not sure about that plugin. But I think reloading page is must after authentication.
#4 Why recount on new site?