How to run Bitcoin Core behind corporate proxy?
Bitcoin doesn't use HTTP for its communications - it has its own specific protocol that runs directly on top of TCP.  So an HTTP proxy like squid won't help.  

If you aren't able to make outgoing TCP connections through your firewall (mainly to destination port 8333) then you'll have to contact your corporate IT people about adding appropriate firewall rules.  The same if you want to be able to enable listening.