Resolving hacked gmail account accessed through live mail

I  was looking at my gmail account using microsoft live mail.  My gmail account was hacked and I cannot now log-on to it through live mail, but I can log on to my gmail account directly via the web.  I have changed my passwords for my gmail account.  My questions for the community are: (1) can the hacker once again gain access to my gmail account via the already breached live mail account if I have changed my password on gmail? (2) How do I stop this from happening (3) How can safely start using live mail again (to look at my gmail account)? Thank you very much for your help.