It's not possible to change what questions you're shown on the homepage (there used to be a nav which allowed you to do something similar, but that was retired. See Retiring New Navigation (beta) in preparation for Navigation 3.0).
You can see the questions you want easily enough through search though (and bookmark the searches if you like).
To see your unanswered questions search for:
user:me is:q answers:0
or if you want questions without an accepted answer (rather than no answers):
user:me is:q hasaccepted:no
For your favorite tags simply replace the user query with
intags:mine is:q answers:0
intags:mine is:q hasaccepted:no
You can find more advanced search options in the help center.