Trending @Accenture; can we open and use our personal GitHub on Accenture laptop? is there any restriction and tracking over this?

Ya there is no issue until and unless they catch you off guard. As per Accenture policy you shouldn’t do it . I suggest don’t push any code to your github account.
Remember they always find a replacement,not a big deal.

I don't think so...just don't post anything related to the project you're working on