1
To use only the week, you can do two things:
1º - Put on startup
defaultView: 'agendaWeek',
this will cause the calendar to initialize in agenda mode.
2º - Remove Month button from header
header: {
left: 'prev,next today',
center: 'title',
right: 'agendaWeek,agendaDay'
},
If you still want to disable allday events, by
'allDaySlot': false
An example can be seen in Jsfiddle
You can find more options on Fullcalendar Docs