how to sync todolist with my google calendar？
Head to Todoist.com, top right corner, gear icon, Settings. From that new pop-up there is an iCal feed URL listed, this is what you need to copy and paste into GCal. As a new subscription.
Can I see my google calendar items inside my todo list will they sync that way?
At this time no they will not. It is only one way sync. If you want to check out Sunrise Calendar it does sync both ways.
Is there a way to integrate the items in Todoist in google calendar (i added todoist in google chrome and can tag mails in Gmail as a task to todoist?
Furthermore, how to change the calendar view in todoist (i.e. Month view,...)
You can integrate Todoist with Google Calendar by subscribing via the iCal feed. Please note that this is a premium only feature.
You can refer to this video on how to set it up: https://www.youtube.com/watch?v=gzGubOy8GuE