This has been answered many times. You can change them using WordPress translation.

I haven’t tried but it will be very very easy because of AnsPress JS. AnsPress trigger event after every action and you can easily use that, for eaxmple: https://gist.github.com/rahularyan/2bbaf37a6e62a9368a36

Use ap_after_new_question hook instead of save_post

Yeh I know about it, will be fixed. Thanks for reporting.

I tried the latest commit, but it does look different and not seems to load the content:

Go to WordPress discussion setting and select AnsPress avatar. That will solve your issue.

Create child theme of AskBug and then copy header.php to new child theme and now remove container class from header.